Citation
Spatio-Temporal Modeling for Peak Events of Seasonal Influenza

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Title:
Spatio-Temporal Modeling for Peak Events of Seasonal Influenza A Case Study in Florida
Creator:
Wang, Ying
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
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Language:
english
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1 online resource (102 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Geography
Committee Chair:
WAYLEN,PETER ROBERT
Committee Co-Chair:
MAO,LIANG
Committee Members:
FIK,TIMOTHY J
MORRIS,JOHN GLENN
Graduation Date:
5/3/2014

Subjects

Subjects / Keywords:
Age groups ( jstor )
Climate models ( jstor )
Diseases ( jstor )
Influenza ( jstor )
Multilevel models ( jstor )
Parametric models ( jstor )
Percentiles ( jstor )
Surveillance ( jstor )
Time lags ( jstor )
Weather ( jstor )
Geography -- Dissertations, Academic -- UF
activity -- ili -- peak-event -- time-lag -- weather
Duval County ( local )
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Geography thesis, Ph.D.

Notes

Abstract:
Influenza is one of the most common infectious diseases with respect to its ability to easily spread from person to person and result in severe complications, or even death. For a typical season, influenza activity often peaks in one, or several weeks which incorporate a high proportion of the cases in an outbreak, and are referred to variously as “peak events”, or “peak weeks”. To address the significance of peak events behind the seasonal nature of influenza outbreaks, multidisciplinary research has been advocated for investigating the impacts of weather conditions on the occurrence of peak events. Taking 16 Florida counties as a study area, this research provides a series of innovative statistical analysis aiming to: 1) derive an unambiguous and practical definition of Influenza-like Illness (ILI) peak events and statistically characterize their properties extracted from limited historic ILI records, including: annual event density, their timing, magnitude over prescribed thresholds, and duration; 2) identify fine-scale time lags between weather fluctuations and ILI peak activity for various age groups in terms of the established definition of peak events; 3) investigate interplay among daily weather conditions, climate divisions, properties of peak events and daily ILI activity during peak events for age-specific groups in Florida based on the identified time lags. The conceptual framework and satisfactory results of this research will aid public health professionals in improving surveillance and determining optimal periods for cost-effective intervention strategies. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2014.
Local:
Adviser: WAYLEN,PETER ROBERT.
Local:
Co-adviser: MAO,LIANG.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2015-05-31
Statement of Responsibility:
by Ying Wang.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Embargo Date:
5/31/2015
Classification:
LD1780 2014 ( lcc )

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1 S PATIO TEMPORAL MODELING FOR PEAK EVENTS OF SEASONAL INFLUENZA : A CASE STUDY IN FLORIDA By YING WANG A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2014

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2 2014 Ying Wang

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3 To my parents

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4 ACKNOWLEDGMENTS Firstly I would like to express my gratitude to my committee chair and my mentor, Dr. Peter R. Waylen. I never fully appreciated the decision of choosing an advisor until I was well underway with my studies and I am thankful for the relationship and store of knowledge I acquired while working with Dr. Waylen I would also feel indebted and grateful for the prolong support from my co chair, Dr. Liang Mao I also recognize and thank the rest of my committee s for providing support and filling in the gaps for other areas of expertise. Dr. Tim Fik generously gave of his time to help me understand the statistical issues of my study. Dr. J. Glenn Morris provided practical advice data and spoke to the large pictur e of the dissertation. Dr. Youliang Qiu gave me inspiration and valuable advice on my analysis. Their suggestions and advice shaped my thinking on medical geography and helped me design my research. W ithout the ir help, my dissertation will not be successfu l. Additionally, without the help of my friends and colleagues I would not have been able to complete my research. While there are many to whom I am thankful, I would like to acknowledge : Sanchayeeta Adhikari Huiping Cai, Wei Feng, Haibing Gao, Zhuojie H uang, Mario Mighty Risa Patarasuk Qiuyin Qi Hanyao Qiu, Caroline Staub Jing Sun, Anna Szyniszewska Jinghui Ying, Jing Yu and Yang Yang. Special thanks to Yi Cao, Beidi Dong and Shuhui Zhang who gave me important support. I would like to acknowledge the support from the geography department. Many thanks are given to Dr. Jane Southworth and Dr. Waylen whose decisions have changed my life trajectory five years ago I would also like to thank Dr. Michael Binford Dr. Ste phen Golant, Dr. Corene Matyas and Dr. Grant Thrall Their support has been i mportant for my graduate research.

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5 This research would also not be possible without support from the Florida Influenza Like Illness Surveillance Network (ILINet) and the Electronic Surveillance System for the Early Notification of Community based Epidemics (ESSENCE) Final ackno wledgement should be dedicated to both my parents, Mr. Ligang Wang and Mrs Xinfen Xu. They always give me the best support they can afford.

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6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 9 LIST OF FIGURE S ................................ ................................ ................................ ........ 10 LIST OF ABBREVIATIONS ................................ ................................ ........................... 11 ABSTRACT ................................ ................................ ................................ ................... 12 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 14 Overarching Research Question s ................................ ................................ ........... 14 Study Objectives ................................ ................................ ................................ ..... 18 2 MODELING PROPERTIES OF INFLUENZA LIKE ILLNESS PEAK EVENTS WITH CROSSING THEORY ................................ ................................ ................... 21 Background ................................ ................................ ................................ ............. 21 Materials and Methods ................................ ................................ ............................ 23 Study Area and Data ................................ ................................ ........................ 23 Methods ................................ ................................ ................................ ............ 24 Definition of peak e vents ................................ ................................ ............ 25 Definition of flu year ................................ ................................ ................... 26 Annual event density ................................ ................................ .................. 26 Timing of events within a flu year ................................ ............................... 27 Event magnitude ................................ ................................ ........................ 27 Event duration ................................ ................................ ............................ 28 Independence of events ................................ ................................ ............. 28 Extrapolation of properties to higher thresholds ................................ ......... 28 Results ................................ ................................ ................................ .................... 29 Annual Numbers of Events, Their Timings and Durations ................................ 29 Magnitudes of Events ................................ ................................ ....................... 30 Extrapolation of Weekly ILI Case s to Higher Levels ................................ ......... 30 Discussion s ................................ ................................ ................................ ............. 31 Comparisons of Definitions ................................ ................................ ............... 31 Geographic Variability and Potential Impacts ................................ ................... 32 Applications ................................ ................................ ................................ ...... 34 Conclusion s ................................ ................................ ................................ ............ 35

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7 3 TOWARD A QUANTITATIVE UNDERSTANDING OF FINE SCALE TIME LAG BETWEEN WEATHER FLUCTUATIONS AND INFLUENZA LIKE ILLNESS PEAK DAYS ................................ ................................ ................................ ........... 48 Background ................................ ................................ ................................ ............. 48 Definition of Infl uenza Peak Days ................................ ................................ ........... 49 Materials and Methods ................................ ................................ ............................ 50 Study Area and Data ................................ ................................ ........................ 50 ILINet data for peak events ................................ ................................ ........ 51 ESSENCE data for peak days ................................ ................................ ... 51 Weather data ................................ ................................ ............................. 52 Methodology Survival Analysis ................................ ................................ ...... 52 Results ................................ ................................ ................................ .................... 54 Time Lags by Age Gro up ................................ ................................ .................. 54 Time Lags by Climate Division ................................ ................................ ......... 55 Discussion s ................................ ................................ ................................ ............. 56 T emporal Scale ................................ ................................ ................................ 56 Impacts of Climate Division ................................ ................................ .............. 56 Impacts of Age ................................ ................................ ................................ 57 Impacts of Threshold (Frequency) ................................ ................................ .... 58 Limitations ................................ ................................ ................................ ........ 59 Conclusion s ................................ ................................ ................................ ............ 60 4 MODELING INFLU ENCES OF METE OROLOGICAL VARIATIONS ON DAILY I NFLUENZAN LIKE ILLNESS ACTIVITY DURING PEAK EVENTS ....................... 66 Background ................................ ................................ ................................ ............. 66 Materials and Methods ................................ ................................ ............................ 67 Study Area and Data ................................ ................................ ........................ 67 Peak Eve nts and Their Properties ................................ ................................ .... 69 Hierarchical Modeling ................................ ................................ ....................... 69 Results and Discussions ................................ ................................ ......................... 72 Resu lts of Modeling ................................ ................................ .......................... 72 Age ................................ ................................ ................................ ................... 73 Properties of Peak Events ................................ ................................ ................ 74 Weather Conditions ................................ ................................ .......................... 75 Conclusion s ................................ ................................ ................................ ............ 77 5 CONCLUSION ................................ ................................ ................................ ........ 85 APPENDIX A SUPPLEMENTARY FIGURE FOR CHAPTER 3 ................................ .................... 90 B SUPPLEMENTARY TABLE S FOR CHAPTER 4 ................................ .................... 92

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8 LIST OF REFERENCES ................................ ................................ ............................... 96 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 102

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9 LIST OF TABLES Table page 2 1 Summary of observed and expected parameters of ILI peak events upon raising the thresholds to the 9 0 th and 9 5 th percentile levels ................................ 37 2 2 Observed and expected parameters of magnitudes upon raising the thresholds to the 90 th and 95 th percentile levels definition 1 ............................ 37 2 3 Observed and expected parameters of magnitudes upon raising the thresholds to the 90 th and 95 th percentile levels definition 2 ............................ 38 3 1 Time lags for age groups at three thresholds ................................ ..................... 62 4 1 Parameter estimates for hierarchical modeling with covariate ( DAY) ................. 79 4 2 Comparisons between model 1 and model 2 for age group 45 64 ..................... 80 4 3 Comparisons between model 1 and model 2 for age group 65+ ........................ 81 B 1 Time lags for age groups at the 80 th percentile ................................ .................. 92 B 2 Model 1 for age group 45 64: parameter estimates for hierarchical modeling with covariates ................................ ................................ ................................ .... 92 B 3 Model 1 for age group 65+: parameter estimates for hierarchi cal modeling with covariates ................................ ................................ ................................ .... 93 B 4 Model 2 for age group 45 64: parameter estimates for hierarchical modeling with covariate s ................................ ................................ ................................ .... 94 B 5 Model 2 for age group 65+: parameter estimates for hierarchical modeling with covariate s ................................ ................................ ................................ .... 95

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10 LIST OF FIGURES Figure page 1 1 Conceptual design and structure of the study ................................ .................... 20 2 1 ILINet five selected counties in Florida ................................ ............................ 39 2 2 Definitions of ILI peak events above threshold ................................ ................... 39 2 3 The mean weekly occurrence of ILI cases in all counties based on defined ................................ ..................... 40 2 4 Comparison of observed and fitted event distribution s in Duval County ............. 40 2 5 Annual event density, timing, and duration at 80 th percentile level in Duval County ................................ ................................ ................................ ................ 41 2 6 C umulative distribution functions (CDFs) of observed magnitudes over 80 th percentile level based on t hree definitions in Duval County ............................... 42 2 7 Forecasted magnitudes over the 90 th and 95 th percentile levels from the 80 th percentile level in Duval County ................................ ................................ ......... 43 2 8 The observed spatial distribution of the parameter k values at three thresholds based on two definitions ................................ ................................ .... 44 2 9 Daily minimum temperature and mean monthly relative humidity in selected cities ................................ ................................ ................................ ................... 45 2 10 Application of annual event density in 18 selected counties in Florida ............... 46 2 11 Application of timing in 18 selected counti es in Florida ................................ ...... 47 3 1 Definitions of ILI peak days and peak events above three thresholds ................ 63 3 2 Study counties within climate divisions in Florida ................................ ............... 64 3 3 Time lags of given age group at 80 th percentile by meteorolog ical factor by climate division ................................ ................................ ................................ ... 65 4 1 Climate d ivision s and study counties in Florida ................................ .................. 82 4 2 Definitions of ILI peak events above the 80 th percentile ................................ ..... 83 4 3 Mean monthly temperature and rainfall in Fl orida ................................ ............... 84 A 1 Time lags of given age group at three thresholds by meteorolog ical factor by climate division ................................ ................................ ................................ ... 91

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11 LIST OF ABBREVIATIONS CDC Centers for Disease Control and Prevention CDF C umulative D istribution F unction ESSENCE E arly Notification of Community B ased Epidemics GPD Generalized Pareto Distribution HLM Hierarchical Linear Model ILI Influenza L ike Illness ILIN ET Influenza Like Illness Surveillance Network

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12 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy S PATIO TEMPORAL MODELING FOR PEAK EVENTS OF SEASONAL INFLUENZA : A CASE STUDY IN FLORIDA By Ying Wang May 201 4 Chair: Peter R. Waylen Co chair: Liang Mao Major: Geography Influenza is one of the most common infectious diseases with respect to its ability to easily spread from person to person and result in severe complications, or even death. For a typical season influenza activity often peaks in one, or several weeks which incorporate a high proportion of t he cases in an outbreak and are referred to variously as or To address the significance of peak events behind the seasonal nature of influenza outbreaks multidisciplinary r esearch ha s been advocated for investigating the impacts of weather conditions on the occurrence of peak events. Taking 16 Florida counties as a study area, t h is research provides a series of innovative statistical analysis aiming to : 1) derive an unambiguous and practical definition of I nfluenza like I llness (ILI) peak events and statistically characteriz e their properties extracted from limited historic ILI records including: annual event density, their timing, magnitude over prescribed thresholds, and duration ; 2 ) i dentify fine scale time lags between weather fluctuations and ILI peak activity for various age groups in terms of the established definition of peak events; 3 ) i nvestigate interplay among daily weather conditions, climate divisions, properties of peak events and daily ILI activity

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13 du ring peak events for age specific groups in Florida based on the identified time lags The conceptual framework and satisfactory results of this research will aid public health professionals in improving surveillance and determin ing optimal periods for cost effective intervention strategies.

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14 CHAPTER 1 INTRODUCTION Overarching Research Question s Influenza, widely known as flu, is a highly contagious and acute respiratory disease. It has the capability of easily spread ing from person to person and leading to severe complications, or even death. For a typical season influenza activity often peaks in one, or several weeks when the number of cases is noticeably higher than other weeks. These weeks incorporate a high proportion of the cases in an outbreak and are referred to variously as or Properties of peak events, such as timing, magnitude, and duration, offer critical implications in disease surveillance, dynamics and control policies (Fleming et al., 1999; Bock et al., 2008). For example, the potential magnitude of peak events provides crucial information about the sca le of an outbreak, and suggests the amount of health resourc es required to respon d to the disease (Cooper et al., 2009) The frequency, timing and duration of peak events offer a statistical basis for long term planning (Cowling et al., 2006 ) Because of t heir significance in epidemiology and planning, the stud ies of such events have received increasing attention in recent years (Greene et al., 2006; Paget et al., 2007; Zaraket et al., 2008; Charland et al., 2008). F ew studies however, have been devoted to statistically defining the peak events of in flu enza and investigat ing the environmental and demographic impacts on the occurrence of peak events To fill the current gap, this research address es several interrelated issues. First, a lthough the concept of peak events is widely used in influenza studies, their workable definition remains under studied T he most common definition of the is the week with the greatest number of weekly influenza cases during an

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15 influenza season an annual maximum ( Smith 1982 ) This definition is widely used and straightforward ; however it has the potential to exclude other events with epidemiological importance and to include an annual maximum in the sample, which really does not constitute an event of epidemiological importance. Valuable information concerning epidemics such as spreading variations, dynamics, and periodicity can be lost from the generally short historic records available by using this definition. Sakai et al. (2004) slightly modified t his approach to incorporate information from weeks leading up to and following the peak event by smoothing weekly reported cases, using a 5 week unweighted moving average of case numbers before selecting the annual maximum of the smoothed data. The risk of this approach is that it reduce s the important characteristics of the largest number of ILI cases in a week and may induc e apparent periodic behavior in what could, in reality, be a random process. More importantly, these existing definitions of peak even ts have little consideration on spatial heterogeneity, such as differences in demographics, and thus the peak events alone are not comparable between geographic areas. L imitations of existing definitions call for a more sophisticated approach employing spa tially differentiated ILI case data which characterizes week ly influenza activity and maximizes the pertinent information that may be extracted from the limited available records, including annual event density (number of events per flu year) their timing, magnitude, and duration Second a monthly/ weekly time lag between weather fluctuations and influenza peak events has been widely discussed but a daily time lag remains unclear The knowledge on time lags between weather fluctuations and influenz a activity is crucial for initiating health planning work ahead of influenza epidemics. Not surprisingly, much

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16 research ha s recently been devoted to investigating influenza related time lags. I t has been reported that influenza epidemic peaks are sensitive to the weekly or monthly averaged temperature and averaged humidity ( Alonso et al. 2007 ; Lowen et al., 2007; Charland et al., 2008 ; Tsuchihashi et al., 2011) For example, h umidity has been found to be associated with seasonal influenza epidemics up to t wo weeks prior to their onset in the continental United States (Shaman et al. 2010). Although previous studies have provided useful information regarding influenza time lags, most of them have focused on coarse temporal resolutions (monthly or weekly) and large spatial scales (either regions or countries), which leads to two major issues. Since the activity of influenza varies by day t here are often lags of several days between the daily weather fluctuations and influenza peak events. Due to the coarse tim e scale, previous week based studies masked the t ime lag between weather and influenza infections. The exact da te of the highest number of case s after a sudden drop in temperature, or change in humidity, for example, is still unknown R esearch findings at large spatial scales are often questioned because of the ecological fallacy or the modifiable area unit problem (MAUP) in geography. E cological fallacy occurs when conclusions derived from a general group are blindly applied to individu al units within that group. The average characteristics of an aggregated group are imposed on individual members belonging to that group (Kramer, 1983). In other words, time lags observed at the country or regional scale may not be valid for intervention w ork at a state or county scale. The lack of understanding fine scale t ime lag s may mislead the forecast of influenza peak events and weaken the effectiveness of timely targeting of high risk groups.

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17 Third some empirical studies have implied a weekly relat ionship between weather fluctuations and influenza peak activity (Greene et al., 2006; Nguyen et al., 2009) ; however, few have explicitly downscaled to a daily relationship. This is because most influenza related datasets are published on a weekly basis for example Influenza Like Illness Surveillance Network (ILINet) to protect individual privacy (CDC, 2013; WHO, 2013) and the daily information is often unavailable T o minimize the impacts of peak event s through early prevention and control measures, st udies have been conducted to determine drivers of the outbreak of peak event s. T he seasonality of influenza peaks indicates the possible roles of weather in affec ting spread of influenza Recently, humidity and temperature have been found to explain the ob served spatio temporal patterns of influenza in studying epidemic outbreaks as they facilitat e the airborne transmission of the virus ( Alonso et al. 2007 ; Lowen et al., 2007; Charland et al., 2008) Other factors, such as s olar radiation dew point and wind speed, and etc. ha ve also been suggested as potential factor s for influenza epidemic outbreak ( Cannell et al. 2006; Sagripanti & Lytle 2007 ; Finkelman et al., 2007 ; Charland et al. 2009). M ost studies have been conducted based on a weekly or bi wee kly scale due to widely adopted weekly reports of ILI activity. However, t he aggregated weekly or bi weekly data prohibits epidemiologists from comprehensively captur ing the impacts of daily meteorological variation on ILI pea k activit y I n addition, l imit ed daily studies (Chan et al., 2010 ; Charland et al. 2009 ) are often restricted to one or a few specific hospitals. The small spatial sample does not furnish reliable estimation for the large spatial scale, such as city, county or even state. I t is difficult to derive more accurate forecast and ef ficient

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18 intervention strategies without understanding the impacts of meteorological factors on daily I LI activity during peak events Study Objective s Following a conceptual design (Figure 1 1) three study objectives based on ILI peak events are listed: 1. Defining ILI peak event and c haracterizing statistical properties of peak events annual event density, their timing, magnitude, and duration 2. Examining daily time lags after weather fluctuations for age specific groups during peak events. 3. Statistically characterizing the association between daily weather conditions and daily ILI activity during peak events for age specific groups in different climate divisions The first study objective defines the p eak events based on the t terms of percentiles of historic weekly ILIs (i.e. defined in the frequency domain); although for epidemiological or planning purposes the peak events could be defined in the magnitude domain. Resul ts extracted above the common 80 th percentile level are extrapolated to the more rarely experienced levels equivalent to the 90 th and 95 th percentiles and compared with the small available sample of historic events that exceed these higher levels. In this way a larger propo rtion of the limited available historic records are utilized to characterize properties of ILI peak events at rarely witnessed levels. Based on the definition of peak event s the second objective conducts a survival analysis of exploring the influences of daily weather fluctuations on ILI peak days It aims to identify the fine scale t ime lags of peak days following weather fluctuations (including: minimum air temperature, average relative humidity, and minimum dew

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19 point) for five age specific groups and five climate divisions at three thresholds (the 80 th 90 th and 95 th percentile levels) T h e third objective present s a timely comprehensive analysis of the influence of meteorological variables on daily ILI activity during peak event s in term s of time lags identified in the second objective It aims to identify the association s among f our meteorological variables ( minimum air temperature, minimum dew point maximum wind velocity and average solar radiation ) the properties of peak event s and daily ILI activity during peak event s for five age specific groups in five major climate divisions of Florida. Th e dissertation is comprised of f ive chapters. Chapter 1 introduce s the o verarching r esearch q uestion s and three s tudy o bjective s The fol lowing three chapters focus on these three study objectives, respectively. Finally, concluding from results of research, Chapter 5 points out the significance of this research and directions for future research.

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20 Figure 1 1 Conceptual design and structure of the study

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21 CHAPTER 2 M ODELING PROPERTIES OF INFLUENZA LIKE ILLNESS PEAK EVENTS WITH CROSSING THEORY Background Influenza, widely known as flu, is a highly contagious and acute respiratory disease. For a typical season influenza activity often peaks in one, or several weeks when the observed number of cases is noticeably higher than other weeks. These weeks incorporate a high proportion of influenza cases in an outbreak and are referred to variously as Properties of rare influenza peak events, such as timing, magnitude, and duration, offer critical implications in disease surveillance, dynamics and control policies (Fleming et al., 1999; Bock et a l., 2008). For example, the potential magnitude of peak events provides crucial information about the scale of an outbreak, and suggests the amount of health resources in response to the disease (Cooper et al., 2009) The frequency, timing and duration of peak events offer statistical basis for long term planning (Cowling et al., 2006) e.g., the risk of more than one such event in a year, and the length of time that each is likely to persist Because of their significance in epidemiology and planning, the stud ies of such events ha ve received increasing attention in recent years (Greene et al., 2006; Paget et al., 2007; Zaraket et al., 2008; Charland et al., 2008). Although the concept of peak events is widely used in influenza related studies, their workabl e definition remains under studied as the week with the greatest number of weekly influenza cases during an influenza season an annual maximum This widely used definition is straightforward ; however it has the pot ential to exclude other events with epidemiological importance that may have occurred in a year, and to include an annual maximum in the sample, which really does

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22 not constitute an event of epidemiological importance. Valuable information concerning epidem ics such as spatial variations, dynamics, and periodicity can not be derived from the generally short historic records by this definition. Sakai et al. (2004) slightly modified this approach in studying influenza like illness ( ILI ). They incorporate d information from weeks leading up to and following the peak event by smoothing weekly reported cases, using a 5 week unweighted moving average of case numbers before selecting the annual maximum of the smoothed data. The risk of this approach is that it o bscures the important characteristics of the greatest number of ILI cases in a week and may induc e apparent periodic behavior in what could, in reality, be a random process. More importantly, these existing definitions of peak events give little considerat ion to spatial heterogeneity, for instance, differences in demographics, and thus the peak events alone are not comparable between geographic areas. The limitations of existing definitions call for a more sophisticated approach employing spatially differe ntiated data which characterize weekly influenza activity and maximiz ing the pertinent information that may be extracted from the limited available records. The se statistical properties of influenza events may all defined by the prescription of a specific threshold To facilitate spatial comparisons, this study defines the threshold in terms of common percentiles of historic weekly ILI case s (i.e. defined in the frequency domain); although for epidemiological or planning purposes the threshold could be defi ned in the magnitude domain, in terms of a total number of ILI cases of particular interest. Results extracted above the 80 th percentile level (0.20 probability of occurring in any week) are extrapolated to the more rarely experienced levels equivalent to the 90 th (0.10 probability) and 95 th percentiles (0.05 probability), and

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23 compared to the small available sample of historic events that exceed these higher levels. In this way a larger proportion of the limited available historic records can be utilized to characterize properties of ILI events above levels commonly witnesse d As the first step in an on going study that seeks to establish associations between ILI peak events and potential factors this study aims to define ILI events and statistically chara cterize the variables of: annual event density, their timing, magnitude over prescribed thresholds, and duration Materials and Methods Study A rea and D ata Florida experienced an average of 2 900 deaths per year from influenza over the past decade (CDC Wonder, 2012) I n 2004 for example, i nfluenza and pneumonia together were the eighth leading cause of death reported by Florida Department of Health (Florida DOH, 2012a) The Florida DOH estimates that an influenza pandemic could infect up to 10 million ( Florida DOH, 2012b). S everal factors encourage the rapid transmission of influenza in the state: its developed national and international tourism industry, high inter and intra national immigration and high proportion of aged population Despite its sub t ropical location and peninsular nature, much of Florida experiences periods of relatively low temperatures and low humidity in winter. A lmost one third of the population including a large proportion of immigrants resides in urban or suburban areas of thr ee southeastern counties Several i nterstate s and 13 international airports including Orlando and Miami bring in tens of thousands of tourists each year (38 million used air travel in 2000 alone) Data employed in this study are obtained from the Influenza Like Illness Surveillance Network (ILINet), which conducts surveillance of weekly ILI outpatient

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24 C) and cough o r sore throat, which may embed influenza along with other conditions, such as colds and pneumonia. However, ILI activity collected through outpatient illness surveillance provides important epidemiologic information for monitoring influenza activity and su pports influenza surveillance (CDC, 2013; Cooley et al., 2008 ). Weekly reports from ILINet are available dating back to 2001 in some counties, however most counties did not have the necessary continuity of reporting at the earliest stages. As representativ es of environmental, demographic, and social conditions in Florida, five counties are selected for extensive study (Figure 2 1) : the lengthy (200 1 2012) historic data from dominantly urban Broward (Fort Laderdale), Duval (Jacksonville) and Miami Dade (Mi am i) counties, as well as short er (2006 2012) records for the Orange (Orlando) and Hill s borough (Tampa) counties Methods Crossing Theory states that the number of crossings of a threshold by a Gaussian process become Poisson distributed the further the thre shold lies from the mean of the process (Rice, 1945; Cramer and Leadbetter, 1967). Results have also been extended to non Gaussian processes (Desmond and Guy, 1991) and can be applied to estimate the characteristics of ILI events. The magnitudes of events over the threshold and their durations can be approximated by an exponential like distribution, such as the Generalized Pareto Distribution (GPD) (Rosbjerg et al., 1992; Keellings and Waylen, 2012) which can represent such data exhibiting with both greater and lesser skew than the exponential itself. In combination with the Possion assumption, it implies Value (GEV) d istribution (Rosbjerg et al., 1992), the properties of which can be

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25 estimated from this approach, if desired. In general, the criteria for adopting a specific distribution are; goodness of fit, a strong theoretical basis, and relative ease of computation a nd interpretation. Although few infuenza related studies have focused on the statistical properties of peak events the proposed approach has been extensively used in studies modeling extremes in various fields, including flood s, stock market returns and daily maximum temperatures (Rosbjerg et al., 1992; Straetmans et al., 2008; Keellings and Waylen, 2012). Definitions of events and the flu year are estabished first, then t he variable s of interest are identified; 1) annual event density (events per year), 2) the timing ( t ) of each event 3) the magnitude of peak event ( q 0 ) during an event when the observed number of weekly cases ( x ) surpasses the thresholds ( q 0 ) and 4) t he duration of events Definition of peak events Although thresholds ( q 0 ) are considered in terms of percentiles of historic weekly ILI case s throughout the study t wo definitions of magnitudes of events are investigated The first includes all weekly ILI count s with magnitudes greater than the prespecified threshold. In Figure 2 2 A for example, all the eight ILI observations greater than the defined threshold would be considered (one or more observations of magnitude per event). The second definition considers only the highest ILI count above the threshold within the period between successive up and down crossings of the threshold level (one observation of magnitude per event) a local maximum. In Figure 2 2 B only the three observations of local maxi ma would be considered. T he properties of ILI peak events are examined above a co mmonly witnessed 80 th percentile level although this approach is applicable for any other reasonably high thresholds

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26 D efinition of flu year Since all ILI cases are likely to be recorded during the winter season, the use of a calendar year definition would arbitrarily bisect a flu season, producing a misleading aggregation of events from two halves of consecutive and distinct seasons. To determ ine when flu is least likely to occur in the historic record (an appropriate point to is analyzed using the mean ( ) and defined fractions of the standard deviations (0.25 0. 32 and 0.5 ) of all weekly ILI cases. If the observed number of weekly ILI cases for one county in one year is greater than the difference between the mean and the defined measure of deviation, an occurrence during that week is confirmed and noted as 1. For each county, the total occurrence of ILI events in a week is calculated by summing the occurrence during th at week in all years. In terms of the mean weekly occurrence in all counties in Florida ( Figure 2 3) Week 29 ( starting July 15) is the week in w hich ILI cases are least likely by this measure, and is thus Annual event density Annual event density is defined as the number of events per flu year. T he probability mass function of the Poisson distribution is : ( 2 1) where M is the number of events in a flu year and is estimated using the method of moments as the mean number of events per flu year : ( 2 2 ) K is the total number of events in N flu years with complete yearly data in the historic records

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27 Timing of events within a flu year Due to the strong seasonal nature of ILI cases, the Poisson distribution is modified to exhibit a time dependent rate of event occurrence ( t ) : ( 2 3 ) w here, P ( m ( t ) = n ), is the probability of having experienced n events up to and including week t and ( t ) is the mean number of events expected up to that time. As influenza outbreaks generally occur in a particular season with some interannual variability, the timings of events is modeled by a Gaussian distribution and ( t ) estimated as ( 2 4 ) where G ( ) is a Gaussian distribution fitted to the observed timing of ILI events, with being the mean week of occur r ences and their standard deviation Event magnitude The distribution of event magnitudes is fit with a GPD ( Rosbjerg et al., 1992; Keellings and Waylen, 2012 ) : ( 2 5 ) where X is the magnitude of the event over the predetermined threshold of interest Completely characterized by a scale parameter, and a shape parameter, k the GPD is a generalization of both the exponential ( k = 0) and Pareto distributions ( k < 0), which provides greater flexibility in matching the heavier ( k < 0) and thinner ( k > 0) upper tails of the distribution. T he parameters are estimated via the method of moments from the sample mean and variance as ( 2 6) and ( 2 7) : ( 2 6 )

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28 ( 2 7 ) Event duration The duration of events is also represented by the GPD (Keellings and Waylen, 2012) : ( 2 8 ) where D is the duration of the event similarly, and are scale and shape parameters, which are estimated via the method of moments by the equations ( 2 6) and ( 2 7), using appropriate means and variances Independence of events A period of two consecutive weeks in which the weekly ILI cases f a ll below the threshold level is employed as the criterion to separate independent peak events O ccasions when weekly cases dropped marginally below the threshold level only to exceed it agai n in the next week are probably the result of the same event Parallel considerations in the definition of flood and heat wave events can be found in Rosbjerg independence criteri on are combined and included in subsequent analysis as if they constitute a single event Extrapolation of properties to higher thresholds An ability to derive the stochastic properties of ILI events above higher, less commonly experienced levels, from the larger sample sizes available at the lower, less epidemiologically important thresholds, would be useful. Any portion of a GPD is itself GPD lower end of GPD and leaving only that portion which rises above the new level.

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29 Estimation of the mean ( 1 ) and variance ( 1 ) of the remaining portion of the distribution yields revised estimates of 1 and k 1 ( E quations ( 2 6) and ( 2 7)) Th e proportion of events expected to exceed the higher threshold represented by the area under the original distribution of magnitudes which lies beyond the new level, yields the parameter, 1 of the Poisson distribution. The probability of the annual number of crossings above the corresponding threshold, or events, can then be estimated. Assuming that the timing and magnitudes of ILI events are independent, the distribution of the timing of censored events should remain unchanged Results A nnual N umbers of Events, T heir T imings and D urations The one sample Kolmogorov Smirnov test is applied to examine the goodness of fit of all models. All results show no significant differences between fitted and observed distributions at the 0.05 level of significance in a ny of the five study counties. Data from the longer term record of Duval County are examine d as an example The assumption of normality of the timing of peak events is reasonable graphically and statistically ( Figure 2 4 ) Historic ILI events are most lik ely to occur during the late fall and early spring (Weeks 20 to 32 of flu year), coincident with conducive meteorological conditions and the early weeks of the spring semester of schools. The Poisson probability function is fitted to the numbers of events exceeding the 80 th percentile level annually ( Figure 2 5 A ) and the non homogeneous Poisson function is applied in order to estimate probabilit ies of experiencing 0, 1, 2, 3 and 4 events up to any week of the flu year ( Figure 2 5 B ). This reproduces well the observed patterns of occurrence during late fall and early spring Taking Week 26 in the flu year (the second week of January) as an

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30 example, the probability of having experienced no peak events up to that time P ( m ( t ) = 0) is 0.43, the probability of e xactly one peak event is 0.36, etc. The probability of an ILI event occurring in a particular week t can be computed as { [ P ( m ( t 1) = 0 )] [ P ( m ( t ) = 0 )]}. The generalized Pareto distribution provides a reasonable approximation to the distribution of the likely durations of events at the 80 th percentile level ( Figure 2 5 C ) Magnitudes of Events Figure 2 6 observed cumulative distribution function ( CDF ) based on either of the two definitions of magnitudes The location parameter, conveys information about the relative magnitude of the cases above the threshold in each county and could be standardized to some base, such as estimated total county population, while the values of k can be compared directly between counties. As expected, the sample sizes derived using definition 1 ( Figure 2 6 B ) are much larger than that using definition 2 ( Figure 2 6 C ). N egative values of the shape parameter k imply that at this relatively low thres hold the upper tail is particularly (larger outliers in the right hand tail of the distribution) in comparison to the bulk of observations Extrapolation of W eekly ILI Case s to H igher L evels The parameters of the above distributions are simply e stimated by application of moment estimators to data extracted at the 80 th percentile level The proposed methodology has the capacity to yield distributions of events exceeding higher, more rarely experienced levels (for example here, the 90 th and 95 th percentile levels) from the larger sample sizes of observations gathered at the lower truncation level ( Figure 2 7). When the critical threshold for Duval county ( Table 2 1) is raised from 10 cases (the 80 th

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31 percentile level ) to 23 (the 90 th percentile le vel), the observed mean annual number of events drops from 1.55 per flu year to 0.91 The GPD fitted to the local maxima of events indicates that 58.5 % of the original 17 events should exceed the increased threshold, yielding an anticipated mean annual num ber of events of 0.90. If the critical threshold is raised to 41 cases (the 95 th percentile level), the observed mean annual number of events drops to 0.45 while 30.8% of the original 17 events (0.48 events per year) are anticipated to exceed this increase d thresho ld. The use of higher threshold levels leads to the exclusion of the bulk of the lower magnitude events, reducing the k Discussion s Grounded in theory, t his approach has the ab ility to describe important statistical properties of such events and provides the necessary degree of flexibility in the definition of ILI event s, while permitting spatial comparisons and the handling of various planning scenarios Once the sui t able probability distributions are identified, the probability of the occurrence of ILI events and their properties can be obtained for further specified purposes Comparisons of Definitions The traditional definition of peak events only captures an annu al maximum (magnitude) in each flu year, but discards other important properties of annual event density and duration significance The proposed approach possesses the benefit of only inclu ding ILI events that meet the level of practical interest while incorporating a potentially larger sample size from the short records currently available. The traditional week applied to Duval County yields 11 observations, while applicat ion of the 80 th percentile

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32 threshold increases the available sample size upon which risk can be estimatesd to 103 using definition 1, and 17 for definition 2. Once estimated, the parameters of the GPD provide the basis for the estimation of propertie s abov e successively higher, more rarely observed, levels of ILI incidence T he threshold of interest can be expressed either in terms of accep table risk (frequency domain) for spatial comparisons, or case numbers (magnitude domain) for planning purposes Although definition 1 of magnitudes yields a larger sample size, the ir obvious serial autocorrelation results in less reliable estimates of the proportion of the observations surviving censoring to higher threshold levels a task which is performed much b etter using magnitudes derived from definition 2. Tables 2 2 and 2 3 display the values of observed and predicted parameters describing the distribution of magnitudes under both definitions above increased truncation levels G eographic V ariability and P ot ential I mpacts T his study provides flexible models that render probabilistic estimates of the variables associated with ILI eve nts that can be adapted to vari ous conditions The robust statistical methodology may be implemente d at any location, no matter t he base (e.g. population), and critical thresholds established. Geographic variability in the parameters indicate differences in the potential influences on the occurrence of ILI peak events. For example, th e observed spatial pattern of the shape parameter k at the 80 th 90 th and 95 th percentile levels in Figure 2 8 suggests that at higher thresholds, more counties exhibit positive values, no matter the definition. Negative k values indicates larger outliers in the right hand tail of the distribution relative to the bulk of the observations. The values of k become less n e gative at higher thresholds because the

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33 comparative magnitudes of the outliers decrease as thresholds increase by progressive censoring. Thi s is particularly noticeable when using definition 1. As a highly contagious and acute respiratory disease, the occurrence and properties of ILI peak events may be influenced by environmental ( mainly weather ) demographic, and social (urban, rural, transpor tation, etc.) factors. Th is approach identifies the average week of ocurrence as late fall to early spring ( W eeks 22 to 30, starting December 10 to February 6 with fairly large standard deviations of 8 to 12 weeks). These observations are supported physica lly by studie s that influenza outbreaks are sensitive to the weekly or bi weekly average temperature s and humidity (Lowen et al., 2007; Charland et al., 2008), particularly low temperature (optimum: 8C) and relative humidity (Lowen et al., 2007; Shaman et al., 2009; Tsuchihashi et al., 2011). Mean temperatures during the coldest month in Florida across t he counties examined range from 10 C to 16 C, suggesting that weather conditions may have impact s on spatial patterns of peak events. However, no clear spatial pattern related to latitude and winter temperatures emerges. As the critical level of ILI cases of interest rises, the mean week of timing for events increases (later in the year) in almost all counties except Broward, implying that peak events with greater weekly ILI cases tend to occur during late winter and early spring. In addition to weather con ditions, each county possess features that encourage influenza tansmission : high population density high proportions of their populations in sensitive age groups, international airports, and ready access t o major interstates, all of which have potentially profound effects on the occurrence of ILI events ( Viboud et al., 2004; Olson et al., 2007; Fang et al., 2008; Rivas et al., 2009; Ertek et al., 2010; Tsai et al., 2010; Fuhrmann, 2010). Similarly

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34 comparative use of public transport and immunization behavi or, may cause differences in the course of epidemics and modif y their space time spread (Lim et al., 2011; Sakai et al., 2004; Paget et al., 2007; Yang et al., 2009). Orange county, for example, exhibits relatively high values of threshold ( q 0 ) and total n umbers of peak events ( K ) compared to the other four counties. This might be explained by its special characteristics of being located in the center of state with comparatively low temperture ( Figure 2 9 A ) and relative humidity ( Figure 2 9 B ) compared to th e two southern counties (Miami Dade and Broward). The major city in Orange county, Orlando, receives tens of thoursands of tourists annually especially during holidays in the late fall and winter, increasing the possibility of influenza transmission for example, compared to the northern county ( Duval ) To better understand the spatial patterns of the derived properties of events the impacts of above factors deserve to be further examined Applications The statistical propertie s of ILI peak events can be spaitio temporally visualized. These visualizations have the potential to deliver information in a efficient manner and assist decision making within public health, such as early warning of influenza peak activity, determining where and when to intervene, increasing accessibility of health facility, and etc. This study mainly discusses two applications. One application aims to visualize the spatial distributions of annual event density for 18 selected counties in Florida. Figure 2 10 describes probabilities of these 18 counties experiencing one peak event ( Figure 2 10A ), two events ( Figure 2 10B ) and three events ( Figure 2 10C ) per flu year. These probabilities are grouped into five classes based on the natural break to maximize the differences between class es. From the Figure 2 10 the probabilities for most counties to experience three events per flu year are smaller than to experience

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35 one or two events per flu year. Only Osceola and Highlands County have high probability to experience three events per flu year. While most of 18 counties, such as Miami Dade, Lake and Broward, tend to experience two events per flu year. A few counties, Alachua and Duval Counties for example, have high probability to experience one event per flu year. Another application is t o visualize the spatial and temporal patterns of timing of peak events, which represents the probability to having two ILI peak events up to Week 25 ( Figure 2 11A ), Week 26 ( Figure 2 11B ), and Week 27 ( Figure 2 11C ). These weeks in flu year are the first t hree weeks in January. ILI peak 2 11A is similar to that in Figure 2 11B. While the probability increases in some northeast counties at Week 27, indicating the possible imp acts of cold weather in January and new semester of schools on ILI activity. These figures can be expanded to the entire Florida in the future. Moreover, properties of peak events can also be visualized with other social or demographic factors for determin ing cost effective planning strategies. Conclusion s This study innovatively applies an established method in hydrology and climatology to the field of epidemiology to describ e the statistical properties of periods during which weekly ILI case s exceed critical thresholds. The strong theoretical basis in Crossing Theory allows for the calculation of the properties of ILI events above various thresholds of interests. The new definition consider s only, and all, o utbreaks of epidemiological interest and permit s estimation of the parameters of the distributions. Another advantage of this approach is that it can be applied to spatially differentiated data to determine and compare risks associated with

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36 peak events, no t defined by a common number of cases, but by a common frequency of outbreak regardless of the base population of the area (e.g. a weekly count that is only experienced in 20%, or 5%, of all the weeks of historic record s in a county). The methodolo gy has the added flexibility of permitting the extrapolat ion of ILI event properties, especially the number of events and magnitude to other critical thresholds that vary in space and are influenced by environmental, demographic, and social factors. With increasing data availability in the future a longer time period and larger sample size can help to better represent these characteristics of ILI events. In the meantime, the potentially limited information contained in the standard (annua l maximum) definition hinders public health professionals in efficiently implementing timing intervention strategies, such as vaccination, quarantine, thus leading to unnecessary socio economic costs. This study can aid public health officials in supportin g influenza surveillance and intervention by including the properties of the variables, annual event density, timing, magnitude, and duration. The d evelopment and testing of the se flexible model s is the first step in an on going study that seeks to establi sh associations between the statistical properties of ILI events and potential environmental factors. These associations can then be combined with vaccination and human mobility to give predictions of influenza transmission and to determine optimal periods to implement influenza vaccination programs among priority regions. I mportantly, the models in this study could be easily extended to other infectious diseases in the further modification

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37 Table 2 1 Summary of o bserved and expected parameters of ILI peak events upon raising the thresholds to the 9 0 th and 9 5 th percentile levels Name Years of record 80 th percentile 90 th percentile 95 th percentile (O/E) (O/E) Broward 11 24.91 10. 76 5.36 2.00 24.33 10.40 3.39 1.64 1.45 ( 72.3 %) 21.75 12.24 2.33 1. 09 0.83 ( 41.5 %) Duval 11 25.06 8. 33 6.35 1.55 28.50 6.88 5.30 0.91 0.90 ( 58.5 %) 25.60 7.83 6.20 0. 45 0. 48 ( 30.8 %) Miami Dade 11 26.21 12.34 6.05 1.73 29.82 10.07 5.27 1.00 0.88 (50.8%) 26.33 9.46 4.83 0.55 0.56 (32.2%) Hillsborough 6 22.63 10.57 7.63 1.33 23. 56 12.65 3.22 1. 50 1. 02 ( 76.7 %) 28.50 8.8 1 5 .25 0. 67 0. 59 ( 49.8 %) range 6 29.90 11. 79 6.50 1 .67 31.40 14.79 6.00 0.83 0. 85 ( 50.9 %) 23.00 10.44 4.67 0.50 0. 45 ( 26.7 %) : m ean of timing ; : s tandard deviation of timing; : m ean duration ; : m ean number of events T able 2 2 Observed and expected parameters of magnitudes upon raising the thresholds to the 90 th and 95 th percentile levels definition 1 Name Years of record 80 th percentile 90 th percentile 95 th percentile q 0 k K q 0 (O/E) k (O/E) K (O/E) q 0 (O/E) k (O/E) K (O/E) Broward 11 2 4.27 0.30 93 4 5.36 5.83 0.29 0.20 54 60 8 6.85 7.19 0.29 0.19 25 41 Duval 11 10 22.52 012 103 23 34.33 25.84 0.06 0.02 51 59 41 44.32 27.50 0.27 0.07 27 29 Miami Dade 11 18 13.76 0.16 102 27 15.55 16.75 0.15 0.05 53 55 34 26.55 17.94 0.06 0.03 27 35 Hillsborough 6 24 20.09 0.10 56 35 30.67 22.93 0.08 0.00 28 33 53 37.85 24.78 0.22 0.04 13 15 Orange 6 69 73.93 0.34 59 114 73.36 51.86 0.64 0.42 29 30 155 49.45 31.25 0.68 0.40 14 14 q 0 : the threshold; : the scale parameter of GPD; k : the shape parameter of GPD; K : the total number of events in total flu years

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38 T able 2 3 Observed and expected parameters of magnitudes upon raising the thresholds to the 90 th and 95 th percentile levels definition 2 Name Years of record 80 th percentile 90 th percentile 95 th percentile q 0 k K q 0 (O/E) k (O/E) K (O/E) q 0 (O/E) k (O/E) K (O/E) Broward 11 2 5.82 0.3 5 22 4 5.75 7.85 0.3 7 0.2 3 18 16 8 5.67 9.50 0.4 0 0.2 1 1 2 9 Duval 11 10 22.69 0.2 4 17 23 31.58 27.59 0.1 6 0.0 03 1 0 1 0 41 55.13 29.82 0.09 0.0 7 5 5 Miami Dade 11 18 12.16 0.26 19 27 14.76 16.42 0.23 0.08 11 10 34 21.99 18.25 0.13 0.05 6 6 Hillsborough 6 24 41.54 0.002 8 35 22.88 41.43 0.05 0.16 9 6 53 46.93 39.60 0.10 0.19 4 4 Orange 6 69 68.15 0.07 10 114 195.14 40.64 1.74 0.25 5 5 155 1921.63 19.54 34.37 0.09 3 3 q 0 : the threshold; : the scale parameter of GPD; k : the shape parameter of GPD; K : the total number of events in total flu years

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39 Fig ure 2 1 ILINet five selected counties in Florida A B Fig ure 2 2 Definitions of ILI peak events above threshold B lue line: weekly ILI cases, red circle: selected peak, and orange line: threshold ( q 0 ) A) Definition 1, B) Definition 2. 0 10 20 30 40 0 5 10 15 Magnitude of ILI Event Week 0 10 20 30 40 0 5 10 15 Magnitude of ILI Event Week q 0 q 0

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40 Fig ure 2 3 The mean weekly occurrence of ILI cases in all counties based on defined Fig ure 2 4 Comparison of observed and fitted event distributions in Duval County Observed cumulative probability of events exceeding 80 th percentile level and fitted cumulative normal distribution. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0 10 20 30 40 Cumulative Probability Week of Flu Year Fitted Observed

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41 A B C Fig ure 2 5 Annual event density, t iming, and d uration at 80 th percentile level in Duval County Timing plots: Probabilities of 0, 1, 2, 3, 4 events having occurred, in Duval County up to any week during the flu year A) Annual event density, B) Timing, C) Duration 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0 1 2 3 4 5 6 Probability Weekly ILI events Possion Observed 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0 10 20 30 40 50 Probability (m(t)) Week of Flu Year 0 1 2 3 4 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0 2 4 6 8 10 12 14 16 18 Cumulative frequency Week GPD Observed

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42 A B C Fig ure 2 6 C umulative distribution functions (CDFs) of observed magnitudes over 80 th percentile level based on t hree definitions in Duval County q 0 : the threshold ILI for each level and K : the number of weekly ILIs exceeding the threshold A) Traditio nal definition, B) Definition 1, C) Definition 2. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0 25 50 75 100 125 150 Cumulative frequency Peak event threshold k =0.134, K =11 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0 25 50 75 100 125 Cumulative frequency Peak event threshold k = 0.116, q 0 = 10, K =103 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0 25 50 75 100 125 Cumulative frequency Peak event threshold k = 0.244, q 0 =10, K =17

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43 Fig ure 2 7 Forecasted magnitudes over the 90 th and 95 th percentile levels from the 80 th percentile level in Duval County 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0 30 60 90 120 Cumulative frequency Forecasted weekly ILI from 80% 90% GPD fit to observed 90% GPD forecast from 80% 95% GPD fit to observed 95% GPD forecast from 80%

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44 A B C D E F Fig ure 2 8 The observed spatial distribution of the parameter k values at three thresholds based on two definitions A) Defintion 1, threshold 80% k B ) Defintion 1, threshold 90% k C) Defintion 1, threshold 9 5 % k D) Defintion 2 threshold 8 0% k E ) Defin tion 2 threshold 90% k F ) Defintion 2 threshold 9 5 % k

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45 A B Fig ure 2 9 Daily m inimum temperature and mean monthly relative humidity in selected cities A) Daily m inimum t emperature B) Mean m onthly r elative h umidity

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46 A B C Fig ure 2 10 Application of annual event density in 18 selected counties in Florida. A) Probability of one event per year, B) Probability of two events per year C) Probability of three events per year

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47 A B C Fig ure 2 11. Application of timing in 18 selected counties in Florida. A) Probability of experiencing two events up to Week 25, B) Probability of experiencing two events up to Week 26 C) Probability of experiencing two events up to Week 27

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48 CHAPTER 3 TOWARD A QUANTITATIVE UNDERSTANDING OF FINE SCALE TIME LAG BETWEEN WEATHER FLUCTUATIONS AND INFLUENZA LIKE ILLNESS PEAK DAYS Background Since the survival and infectivity of influenza virus is sensitive to meteorological factors, weather fluctuations often foreshadow the outbreak of influenza, such as the drop in temperature and humidity ( Charland et al., 2008; Firestone et al., 2012 ; Lowen et al., 2007). The knowledge on time lags between weather fluctuations and influenza activity is crucial for initiating health planning work ahead of influen za epidemics. Not surprisingly, a lot of research efforts have recently been devoted to investigating influenza related time lags. For example, Shaman et al. (2010) observed a marked humidity change up to two weeks prior to the onset of seasonal influenza epidemics in the continental Unite d States. The research done by T ang et al. (2010) demonstrated that the incidence of influenza was correlated with meteorological conditions with lags of one or two weeks in five study countries. Murray and Morse (2011) fo und that the outbreak of human H5N1 influenza in Egypt and Indonesia occurs 6 8 weeks following significant changes of meteorological conditions. More recently, Tamerius et al. (2013) reported a time lag of approximately one month between temperature, humi dity and influenza peaks across temperate and tropical regions. Although previous studies have provided valuable information regarding influenza time lags, most of them have focused on coarse temporal resolution (by week or month) and large spatial scale (by region or country), which leads to two major issues. The first issue concerns the temporal resolution. Previous monthly or weekly based studies failed to capture time lags in days between weather fluctuation and influenza

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49 outbreaks. A possible reason is that most influenza reports are published on a weekly basis to protect individual privacy (CDC, 2013; WHO, 2013), for example, the Influenza Like Illness Surveillance Network (ILINet) and the daily information is often unavailable. Immediate response c an hardly be implemented without knowing the exact days between weather fluctuations and the possible influenza outbreak. Second, research findings at large spatial scales are often questioned because of the ecological fallacy or the modifiable area unit p roblem (MAUP) in geography. The ecological fallacy occurs when conclusions derived from a general group are blindly applied to individual units within that group. The average characteristics of an aggregated group are imposed on individual members belongin g to that group (Kramer, 1983). In other words, time lags observed at the country or regional scale may not be valid for intervention work at a state or county scale. To date, these issues have not been properly addressed and remained unclear due to the la ck of data on daily influenza activity. The newly available Electronic Surveillance System for the Early Notification of Community based Epidemics (ESSENCE) is a system that organizes electronic emergency department (ED) data at a daily scale for the purpose of syndromic surveillance (ESSENCE User Guide, 2010) Taking advantage of the ESSENCE data this article aims to fill the aforementioned research gaps by identifying daily scale time lags between weather fluctuations and influenza peak days by age group and by climate division, taking the Florida state as a study area Definition of Influenza Peak Days The peak day of influenza in this study is defined in the frequency domain by the prescription of a specific threshold, different from the common definition in the

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50 magnitude domain on basis of a total number of influenza like illness (ILI) cases of particular interest is used to define peak activity, in terms of common percentiles of historic weekly ILI case s ( e.g the 80 th percent ile ) because influenza activity is widely reported on a weekly basis. Those weeks with total number of ILI cases over the threshold are called epidemic events, or epidemiological events ( Figure 3 1). Among these epidemic events, the one with the greatest total number of ILI cases is defined as a peak event, which refers to a week whose total number of ILI cases reaches the maximum between a pair of successive up and down crossings of a threshold level. In addition, a period of two consecutive weeks in whi ch the weekly ILI total falls below the threshold is used to separate independent peak events. Within a peak event, the influenza peak day is then defined as the day with the greatest number of ILI cases within a peak event, which possesses the largest pro portion of total ILI cases in a peak event. Three common used thresholds are applied in this study, the 80 th 90 th and 95 th percentiles. As illustrated in Figure 3 1, there are two peak events at the 80 th percentile level, one peak event at both the 90 th a nd 95 th percentiles. For each peak event, the peak day within it can be easily identified and then used in subsequent time lag analysis, for instance, Day 3 in Figure 3 1 is the peak day during corresponding peak event Materials and Methods Study Area and Data Due to data availability, 16 counties in Florida, USA, are selected as study area, which represents major climate divisions and a cross section of demographic characteristics ( Figure 3 2). Florida is divided into seven climate divisions by the

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51 Nat ional Climatic Data Center (NCDC) for the purpose of assessing large scale climate features from a long period perspective (Guttman and Quayle, 1996). Divisions 5 and 6 are combined into one division in this study, denoted as Division 5 6, since Division 6 only covers a narrow shape of east coast of Florida ( Figure 3 2). Division 7 (the Keys) is not taken into consideration due to its small population. Among these major climate divisions, Divisions 1 and 2 are the two coldest divisions, whereas Division 5 6 is the hottest. Different from temperature patterns, the patterns of precipitation are more complicated in Florida, varying in seasons. From late fall to early spring (the major influenza season), Division 1 is the most humid area of the State, while Divi sion 5 6 is the driest. Then, during summer, Divisions 1 and 5 6 are the most humid areas, whereas Division 2 is the driest. In fall, the area with highest amount of precipitation is Division 5 6 and the areas with lowest precipitation are Divisions 1 and 2 ILINet data for peak events To identify peak events, weekly ILI data are acquired from the Influenza Like Illness Surveillance Network (ILINet) The ILINet conducts surveillance for ILI in collaboration with the Bureau of Epidemiology at Florida State H ealth Department and the Centers for Disease Control and Prevention (CDC) (FDOH, 201 3 ). The weekly Week 15, 2012 are included in subsequent analyses. For a sensitivity anal ysis, the peak events are identified for each of the 16 counties based on following three thresholds, the 80 th 90 th and 95 th percentiles ESSENCE data for peak days For each identified peak event, the daily ILI cases of 14 consecutive days are obtained from the ESSENCE database, including seven days prior to the peak event

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52 and seven days within the peak event. Components of the daily data from the EDs include several age, chief complaint, date of visit, time of visit and etc The daily ILI cases are further separated into five age groups (0 4, 5 17, 18 44, 44 64, and 65+) to eliminate the confounding effects of age. The peak day by age grou p then can be detected within a peak event, as the day with the highest ILI cases, for time lag analysis Weather data To link influenza peak days with weather fluctuations, daily meteorological data are extracted from weather stations ( Figure 3 2) of Flo rida Automated Weather Network (FAWN, 2013) Three meteorological factors are selected to represent weather fluctuations, including: the minimum temperature, average relative humidity and minimum dew point. Their roles in influenza transmission have been w idely recognized (Yassine et al., 2010; Shaman et al., 2011; Shoji et al., 2011; Davis et al., 2012). The daily weather records are organized as a serial of 14 days paired with the 14 days associated with each identified peak event. The paired weather and ILI cases are then input into a survival analysis to estimate time lags, discussed as follows Methodology Survival Analysis Generally speaking, survival analysis is a set of statistical techniques for analyzing time to event data such as the data with time to death or time to onset of a disease (Klein and Moeschberger, 2003). The outcome of interest is the time duration to an event of interest, denoted as T a non neg ative random variable representing the waiting time until the occurrence of an event. The distribution of T can be estimated by the hazard function h ( t ) and cumulative hazard functions H ( t ) :

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53 ( 3 1) ( 3 2 ) where the hazard function h ( t ), also known as the hazard rate, or the failure rate, indicates the instantaneous probability per time unit for the event to occur, given that t The numera tor of h ( t ) is the conditional probability that the event occurs in the time interval ( t t + ), and the denominator is the width of the interval. For small the hazard rate can be expressed as the density of events at t divided by the probability of surviving to that duration without experiencing the event. The cumulative hazard H ( t ) is the integral of hazard function. Relevant to this study, the hazard event refers to the defined ILI peak day as aforementioned. Within the corresponding 14 days, the days before the peak day are used to detect a marked change of meteorological observations, for example, to identify the da y with a drop in temperature. This study applies the easiest way to define such a day, which is to identify the day with the minimum meteorological conditions (e.g. minimum temperature, average relative humidity or minimum dew point). This day is then set to be the beginning point of survival analysis. The duration from the beginning point to the peak day is estimated for h ( t ) and H ( t ). The time lag T is estimated as : ( 3 3 ) w here arg max represents the argument of the maximum and h ( t ) is the hazard function. This equation gives the value of t for which h ( t ) attains its largest value. In other words, the time lag T is estimated by the time duration that the hazard rate reaches the maximum. The hazard function h ( t ) and cumulative hazard functions H ( t ) for ILI peak

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54 events at the 80 th 90 th and 95 th percentiles are estimated for five age specific groups and five climate divisions respectively Results Time Lags by Age Group Table 3 1 shows the time lags by age group and by meteorological f actor at the three thresholds. At the threshold of the 80 th percentile, time lags range from 3.2 to 5.1 days, varying across age groups and meteorological variables. The elderly people over 65 years old are most sensitive to weather fluctuations because th e time lag of this age specific group is the shortest among all age groups, especially in terms of minimum temperature (3.4 days) and minimum dew point (3.2 days). Except for average relative humidity, the age group 5 17 has shorter time lag (3.9 days) tha n group 65+ (4.0 days). Another sensitive age group is group 0 4, which has relatively short lags compared with other three age groups. However, this age group has the longest time lag of 5.1 days when relating to average relative humidity. The age group 1 8 44 seems to be the least sensitive group to weather fluctuations, displaying relatively long time lags. Three weather conditions play different roles in affecting time lags of age groups. When compared to drops of minimum temperature and dew point, the d rop in relative humidity has fewer impacts on ILI peak days, in terms of relatively long time lags presenting by all five age groups. For example, in the age group 65+, time lags after the drop in minimum temperature and dew point are around 3 days, while the time lag after the drop in average relative humidity is around 4 days The increase of threshold in the definition of peak event does not significantly affect time lags. Time lags range from 3.2 to 5.2 days at the 90 th percentile and from 3.1 to 6.8 da ys at the 95 th percentile, similar to those at the 80 th percentile. Only one

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55 interesting difference has been observed when the time lags at the 90 th and 95 th percentiles associate with average relative humidity. That is, the age group 5 17 has the longest time lag of 5.2 days compared with other four groups at the 90 th percentile and the group 18 44 has the longest time lag of 6.8 days compared with other grou ps at the 95 th percentile, which are different from observations at the 80 th percentile Time Lags by Climate Division Time lags also vary over space. Figure 3 3 displays time lags of given age group influenced by three meteorological factors at the thres hold of the 80 th percentile. These time lags ranging from 1 to 13 days are estimated based on cumulative hazard functions at five divisions at the 80 th percentile. In response to drops of the three meteorological factors, the time lag of group 0 4 tends to be shorter in Divisions 1 and 4, while age groups 5 17 and 65+ have relatively short lags in Division 3. All groups experience longest time lags in Division 2, except group 18 44 with longest time lags in Division 3. The lags for five age groups seem to b e consistent in Division 5 6 between 4 and 6 days. Similar results can be found at the 90 th and 95 th percentiles. However, some differences have also been observed. In Division 2, time lags at the 90 th and 95 th percentiles for older age groups relevant to three meteorological factors tend to be shorter. For example, the lag of age group 65+ in response to the drop in minimum temperature at the 90 th percentile (Fig ure A 1 in Appendix A ) and the lag of age group 44 64 (Fig ure A 1I in Appendix A ) in response to the drop in minimum dew point at the 95 th percentile are the shortest in Division 2. The lags of five age groups are relatively consistent in five divisions related to average relative humidity (Fig ure A 1E and Fig ure A 1F in Appendix A )

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56 Discussion s T emporal S cale Time lags have been discussed currently at different temporal scales, for example, monthly scale ( Tamerius et al., 2013 ), bi weekly scale ( Murray and Morse, 2011 ) or weekly scale ( T ang et al., 2010). In this study, time lags are identified b etween three to seven days in five age groups in response to the drops in three meteorological conditions, which is much shorter than other previously studies. One of the major reasons lies in that the coarse time scale applied in these studies prevent est imating associations between meteorological conditions and ILI peaks at a fine scale. Another possible reason is the timing of influenza activity focused in studies. This study focuses on peak event, while other studies concentrate on the onset of ILI epid emics ( Tamerius et al., 2013) or the outbreak of influenza activity ( Murray and Morse, 2011) The different definitions of timing may result in various time lags. Additionally, models i n the limited studies of daily scale (Chan et al., 2011) have a potenti al limitation that they are constructed for several specific hospitals. Thus, these models may be unrepresentative for large areas. As an improvement, this study examines time lags at a daily scale with relatively representative study area, ranging from th ree to seven days (Table 3 1) in various age groups, meteorological conditions and thresholds. These findings are capable of capturing the dynamics of ILI activity in response to the drops in meteorological conditions Impacts of C limate D ivision Regarding to the spatial scale, a fine spatial scale is called for a better understanding of the association between metrological conditions and peak events (Lowen et al., 2007). This study takes climate divisions into consideration, which has

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57 never been d iscussed. The identified time lags vary across climate divisions, implying the potential influences of geographic variability on ILI peak activity Transmission rates of various influenza viruses are found to be higher at relatively low temperature (Tang e t al., 2010; Lowen et al., 2007; Murray et al., 2011; Irwin et al., 2011). M ean average daily temperatures during January, the coldest month of the year drops to a lower 10C in Divisions 1 and 2, approaching the optimum temperature for flu transmission (8 C). Accordingly a low temperature has great potential to influence time lags, especially in Northwest Florida. In addition, the impacts of relative humidity and dew point on time lags may be affected by an abundance of precipitation in Florida. As one of the wettest states, Florida has approximately on average 1.37 meters of precipitation annually ( Winsberg et al., 2003). The Panhandle (Division 1) is the wettest region in Florida from late fall to early spring (the major flu season). High humidity in the air may reduce the survival time of influenza viruses. Besides, t ime lags in Divisions 3 and 4 are relatively short, especially when peak events are defined at the 80 th percentile. Time lags are one to two days shorter in these two divisions than in Divisi on 5 6. The possibility of transmission through human cont act and mobility in central and so utheastern Florida due to busy road network and air travel may help to explain these variations and deserve further attention Impacts of Age As prior research has demonstrated, a ge is a significant contributor to influenza infection (Longini et al., 1988; Olson et al., 2007; Riley et al., 2011; Gilca et al., 2011). Young children are at high risk of infect ion and adults 65 years and older exhibit great potential to develop severe symptoms and even die from influenza related diseases (Viboud et al., 2004; Ertek et al., 2010; Gilca et al., 2011; Zhang et al., 2011). However,

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58 few studies have examined time lag s by age group. This study attempts to identify time lags resulted from age variations. As shown in Table 3 1, the estimated time lags corresponding to the decreases of three meteorological conditions in the five climate divisions vary by age In this study, two high risk groups, children (0 4) and adult (65+) reveal relatively short lags, whereas the adult group (18 44) displays the longest lags following weather fluctuations. It worth mentioning that age group 65+ apparently has the shortest lags amon g the five studied age groups. Besides, the lifestyle of adults 65 years and older in Florida may also have influences on this observed pattern. This is because Florida has higher percentage of adults 65 years and older and senior centers and communities compared with other states. The concentrated high risk populat ion leads to quick transmission of influenza Impacts of Threshold (Frequency) This study identifies time lags based on three common thresholds, the 80 th 90 th and 95 th percentile levels. The i ncrease of threshold in defining peak event does not significantly affect time lags, indicating the limited impacts of threshold on time lags. The possible reason is that the peak events at three thresholds (the 80 th 90 th and 95 th percentiles) are extract ed from the same historical records. The selected samples of peak events are similar at different thresholds, which minimize the impacts of thresholds on time lags. There are still some differences at three thresholds. For example, the least sensitive age group associated with average relative humidity changes with the increase of thresholds. The age group 18 44 presents the longest time lag of 6.8 days at the 95 th percentile, compared with the least sensitive age group 5 17 at the 90 th percentile and group 0 4 at the 80 th percentile. Besides, elder age groups 45 64 and 65+ are more sensitive to weather fluctuations at higher thresholds, especially in

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5 9 Division 2 with relatively cold winter. These findings suggest the important role of a ge in the spread of in fluenza. More importantly, such pattern is obviously presented by the increase of thresholds, or peak events with remarkable high magnitudes (number of ILI cases) indicating the high risk age groups in the severe outbreak of influenza epidemics. Limitatio ns There are several limitations of investigation. One limitation is that this study only analyzes five climate divisions in Florida due to the available data, all belonging to subtropical and tropical climate. Therefore, it is important and necessary to r eplicate the study and assess the impacts of geographic variability in other climate divisions in the future to reach a firm conclusion. The second limitation is that this study adopts the day with the lowest value of meteorological conditions as the begin ning point. For example, the day with the lowest minimum temperature before the peak event is the beginning point. This is because the lowest value is easy to measure and identify. In fact, beginning points could be defined based on other alternative crite ria, for example, specifying a value to measure and define the drop in weather conditions. This issue of refining the beginning point when conducting survival analysis deserves special attention in future research. Third, this study only applies three com mon thresholds, the 80 th 90 th and 95 th percentile levels. However, t he threshold used for defining peak event may vary in regions and diseases, and then can be extended to other levels of medical interest in the future The final limitation is about the data sources, mainly the ILINet and ESSENCE. The data of the ILINet are reported by sentinel providers once a week,

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60 including the ILI cases and laboratory confirmed cases. However, the coverage of sentinel providers in Flo rida is still low, especially in early 2000s, although it increases gradually now. In other words, the high ILI cases found in recent years may not be completely resulted from high ILI activity, but from the increasing number of sentinel providers. The dat a of the ESSENCE are collected from EDs once a day using chief complaint information. Different from the coverage of sentinel providers for the ILINet, the coverage of EDs for the ESSENCE is much higher, around 75% hospitals in Florida. The collected ILI c ases from EDs, however, are normally severe cases. These severe cases may not be applied to all ILI activity. Conclusion s This study applies the ESSENCE data and survival analysis to quantify fine scale time lags between weather fluctuations and the onset of ILI peak days in Florida. Through defining peak events at three thresholds from the frequency domain, this study finds evidence that the influences of fluctuations of meteorological conditions (minimum temperature, average relative humidity, and minimu m dew point ) on ILI peak days vary with age (3.2 5.1 days, 80%; 3.2 5.2 days, 90%; 3.1 6.8 days, 95%). Age group 65+ is the most sensitive group to weather fluctuations, with a shorter time lag of one to two days than group 18 44. Time lags also vary over space. People in high temperature and abundant precipitation area (e.g. Division 5 6) experience a longer time lag of one to two days than that does in relative low temperature and low precipitation area(e.g. Division 3). Among three weather conditions, a verage relative humidity has the least impact in affecting influenza activity.

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61 The research outcomes would contribute to the current knowledge of influenza diseases in following two folds. First, as one of the first attempts to estimate time lags between w eather fluctuations and ILI peak activity at a fine spatio temporal scale, this study minimizes the impacts of ecological fallacy and fills the void that only coarse time lags (monthly/weekly lags) are available. Second, as one of the earliest studies to u tilize the ES SENCE data, this study takes advantage of its wide coverage and detailed data to understand ILI activity and associated impacts. This study serves as an example of applying ESSENCE to explore the relationship between disease and environment. F rom a practical point of view, based on the definition of peak events, the fine scale time lags identified in the study can be used to improve surveillance systems and to determine optimal periods for implementing cost effective influenza vaccination programs among high risk groups and areas

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62 Table 3 1 Time lags for age groups at three thresholds Thresholds Age groups Minimum Temp (95% CI) Average RH (95% CI) Minimum DP (95% CI) 80% 0 4 3. 6 (3.3, 3.8) 5. 1 (4.8, 5.3) 3. 6 (3.3, 3.8) 5 17 3. 8 (3.5, 4.0) 3. 8 (3.6, 4.1) 4. 1 (3.8, 4.3) 18 44 4. 2 (3.9, 4.2) 4. 6 (4.3, 4.8) 4. 0 (3.8, 4.2) 45 64 3. 8 (3.5, 4.0) 4. 1 (3.8, 4.3) 4. 3 (4.0, 4.5) 65+ 3. 4 (3.1, 3.6) 4.0 (3.8, 4.2) 3. 2 (2.9, 3.4) 90% 0 4 3. 5 (3.2, 3.7) 5.1 (4.9, 5.3) 3.4 (3.2, 3.6) 5 17 3. 8 (3.5, 4.0) 5. 2 (4.9, 5.4) 3.6 (3.4, 3.8) 18 44 4. 8 (4.6, 5.0) 5. 1 (4.9, 5.3) 4.0 (3.8, 4.2) 45 64 4. 2 (3.9, 4.4) 4.0 (3.8, 4.2) 3.7 (3.5, 4.0) 65+ 3.2 (3.0, 3.4) 4.9 (4.7, 5.1) 3. 8 (3.5, 4.0) 95% 0 4 3.3 (3.1, 3.5) 5.3 (5.1, 5.5) 4.0 (3.8, 4.2) 5 17 4. 2 (3.9, 4.4) 4.6 (4.4, 4.8) 5.0 (4.8, 5.3) 18 44 4. 9 (4.6, 5.1) 6. 8 (6.5, 7.0) 5.0 (4.7, 5.2) 45 64 3.5 (3.3, 3.7) 4.8 (4.6, 5.0) 4. 4 (4.1, 4.6) 65+ 3.1 (2.9, 3.4) 5. 3 (5.0, 5.5) 3. 7 (3.4, 3.9)

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63 Fig ure 3 1 Definitions of ILI peak days and peak events above three thresholds. The insert shows the daily ILI activity during the peak event. The peak event is defined by the ILINet data and the peak day is identified by the ESSENCE data 0 10 20 30 40 50 60 70 80 90 100 110 0 5 10 15 20 25 30 35 ILI cases Week The 95 th percentile The 90 th percentile The 80 th percentile Peak event Epidemic event Data from the ESSENCE Data from the ILINet 0 5 10 15 20 25 1 2 3 4 5 6 7 ILI cases Day Peak day

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64 Fig ure 3 2. Study counties within climate divisions in Florida

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65 Fig ure 3 3 Time lags of given age group at 80 th percentile by meteorological factor by climate division A) Minimum Temp, B ) Minimum RH, C) Minimum D P

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66 CHAPTER 4 MODELING INFLUENCES OF METE OROLOGICAL VARIATIONS ON DAILY I NFLUENZAN LIKE ILLNESS ACTIVITY DURING PEAK EVENTS Background Annual activity of influenza like illness (ILI) usually peaks during one or several of the most easily identified features in a given season (Charland et al., 2009). Properties of peak events could offer critical implications in disease surveillance, dynamics and control policies (Fleming et al., 1999; Bock et al., 2008). For example, the potential magnitude of peak events ind icates the scale of an outbreak, and suggests the amount of health resources required for the public health ( Cooper et al., 2009). It is not surprising that the peak events have received increasingly attention in recent years (Greene et al., 2006; Zaraket et al., 2008; Charland et al., 2008). For early prevention and control of influenza, lots of efforts have been devoted to explore possible drivers of the onset of influenza peaks (Alonso et al., 2007; Charland et al., 2008; Finkelman et al., 2007; 2007; S agripanti & Lytle, 2007). Humidity and temperature have been found to facilitate the airborne transmission of the virus (Alonso et al., 2007; Charland et al., 2008; Lowen et al., 2007). Studies also suggest solar radiation as a potential factor for influen za epidemic outbreaks, because exposure to sunlight at various times has impacts on innate immunity and airborne virus (Cannell et al., 2006; Charland et al., 2009; Finkelman et al., 2007; Sagripanti & Lytle, 2007). A majority of current studies have conce ntrated on weekly or bi weekly scale, because the ILI activity is often reported on a weekly basis by health authorities, such as the Centers for Disease Control and Prevention (CDC). However, it is widely known that the activity of influenza varies by day because of the characteristics of virus. Due to the coarse

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67 time scale, these aggregated weekly or bi weekly data prevent epidemiologists from understanding the impacts of daily meteorological variation on ILI activity (Murray and Morse, 2011; Tamerius et al., 2013), especially ILI dynamics in peak events. There are limited numbers of daily scale studies on the influences of meteorological variations on ILI activity (Chan et al., 2010; Charland et al., 2009). However, they are usually restricted to one or several specific hospitals. The small sample size cannot provide reliable estimation of ILI activity for large spatial scales, such as city, county or state. The lack of daily forecast models may mislead the forecast of influenza peak events and weaken the effectiveness of intervention strategies. Taking advantage of the Electronic Surveillance System for the Early Notification of Community based Epidemics (ESSENCE) data, which is organized on a daily basis, this study builds upon an understanding of associ ations among the daily ILI activity during peak events, meteorological conditions, and statistical properties of peak events Materials and Methods Study Area and Data In the past decade, an average of 2,900 people died from influenza per year in Florida ( CDC Wonder, 2012 ). There are several factors that may suggest the readily transmission of influenza in the state, such as a large tourism industry, immigration and a high proportion of elderly population. More importantly, much of Florida experiences perio ds of relatively low temperatures and low humidity in winter even as sub tropical location. In this study, 16 counties are selected as representatives of six major climate divisions in Florida (except Division 7 Keys with small population) ( Figure 4 1). Climate divisions from the National Climatic Data Center (NCDC) are used for assessing large scale climate features from a long period perspective (Guttman and

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68 Quayle, 1996). Due to a narrow shape of east coast, Climate Division 6 is combined with Division 5. Therefore, this study discusses five climate divisions. Among these divisions, Divisions 1 and 2 experience the lowest mean average temperatures around lower 10C during the coldest (January) month in Florida, while Division 6 have the highest mean ave rage temperatures around 15.6C. Different from temperature patterns, Divisions 1 and 6 are the wettest area of Florida Two sets of ILI data are used for this study. One is obtained from the Influenza Like Illness Surveillance Network (ILINet), which cond ucts surveillance of weekly ILI outpatient cases (Florida DOH, 2012). These weekly ILI data between week 29, 2006 and week 15, 2012 are used to identify peak events and associated properties for 16 counties of Florida. The second data set describes corresp onding data of daily ILI cases (a series of 14 days) for each peak event acquired through the ESSENCE, which collects electronic emergency department (ED) data for syndromic surveillance in communities (ESSENCE User Guide, 2010). Currently, ED data in the ESSENCE of Florida is de identified from 163 hospitals and urgent care centers (ESSENCE User Guide, 2010) and updated once a day. The reported number of daily ILI visits and their ages in each county during the selected peak events are included in the anal ysis. The daily ILI visits are further separated into five age specific groups (0 4, 5 17, 18 44, 45 64, and 65+) to estimate the impacts of population demographics on ILI activity in Florida. The d ata of d aily meteorological conditions for 16 counties are obtained from weather stations of the Florida Automated Weather Network ( Figure 4 1 ) including daily minimum air temperature (MINT), minimum dew point (MINDP), average solar radiation

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69 (AVGSR), and maximum wind speed (MAXWS). This study uses d ew point in dicating the amount of moisture in the air as a surrogate for relative humidity because it is independent of air temperature (Davis et al., 2012 ; Shaman et al., 2009) Peak Events and Their Properties is introduced first, in terms of commo n percentiles of historic weekly ILI case s Weeks with total number of ILI cases over a threshold are epidemic events, or epidemiological events. Among them, the one with the highest total number of ILI cases is the peak event, as the week whose number of ILI cases reaches the maximum between a pair of successive up and down crossings of a threshold level In addition, a period of two consecutive weeks in which the weekly ILI total falls below the threshold level is used to se parate independent peak events A common ly used threshold the 80 th percentile is applied in this study. For example in Figure 4 2 two critical events with maximum magnitudes between successive up and down crossings of the 80 th percentile are considered as peak events This definiti on has the advantage of statistically characterizing properties of peak events, such as annual event density, their magnitude and duration. These three properties are represented by parameter shape parameter k and shape parameter k respectively and estimated from the peak events in each of the 16 counties The impacts of these three properties on daily ILI activity in peak events are examined in the subsequent analysis Hierarchical Modeling A two level hierarchical model is implem ented to examine associations among the daily ILI activity during peak events, weather conditions, and properties of peak events For each peak event a series of 14 day daily ILI cases are extracted, which are seven days before the peak event and seven da ys in the peak event. The l evel 1 model

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70 determines the change of daily ILI activity within each peak event, suggesting the trend of daily ILI visits from age specific groups over corresponding 14 days during each peak event. The l evel 2 model plots differe nces between peak events (Bryk & Raudenbush, 1987). Let y ti denote the number of ILI visits during the i th peak event on the t th day for each of the five age specific groups, where i n and t n is the total number of identified peak events. The time lags between weather conditions and influenza peak days are considered in the analysis for pairing daily weather conditions with daily ILI cases on the t th day (see Table B 1 in Appendix B ). These time lags vary in age groups and weather conditio ns (only for minimum temperature and minimum dew point), denoted as l This study assumes daily ILI visit s at EDs to follow a Poisson distribution (Chan et al., 2010). The daily variability of the number of ILI visits at the level 1 model is represented as : ( 4 1 ) where the parameter ti is the expected risk for the corresponding peak event and time interval. Two models are applied to compare the impacts of climate divisions and properties for peak events on ILI activity. The first model (model 1) only considers daily weather conditions and the second model (model 2) incorporates climate divisions and properties for peak events. Both models have the same level 1 model, which is expressed as : log( ti ) = 0 + 1 DAY ti + 2 MINT t l i + 3 MIN DP t l i + 4 AVG SR ti + 5 MAXWS ti + e ( 4 2 ) For i n peak event s, where DAY ti is the time unit for each peak event i t 14 and MINT t l i MIN DP t l i AVG SR ti and MAXWS ti are time varying covariates at

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71 level 1 for each individual event i Subscript t l represents a time lag of l days, indicating the minimum temperature and minimum dew point of the t l th day. e is the errors independent and normally distributed with common variance 2 F or the model 1 without the impacts of climate divisions and properties of peak events, the level 2 is : 0 = 00 + r 0 1 = 10 2 = 2 0 3 = 3 0 4 = 40 5 = 5 0 ( 4 3 ) For the model 2 with the impacts of climate divisions and properties for peak events, the level 2 model is : 0 = 00 + 0 1 + 0 2 k + 0 3 + r 0 1 = 10 2 = 21 CD 1 + 22 CD 3 + 23 CD 4 + 24 CD 5 6 3 = 31 CD 1 + 32 CD 3 + 33 CD 4 + 34 CD 5 6 4 = 40 5 = 5 0 ( 4 4 ) Variables at level 2 model are the parameters for differences between peak events (slope or growth). Division 2 is designed as a reference for its relatively low temperature and moderate precipitation compared with other four climate divisions. CD 1 CD 3 C D 4 and CD 5 6 are dummy variables for respective climate division. stands for the parameter for annual event density as the mean number of events per flu year. k

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72 and represent shape parameters respectively describing magnitudes and durations at the 80 th percentile level. These three parameters for properties of peak events are used to measur e contextual characteristics of counties. 01 02 and 03 are the effects of k and on the intercept. 10 is the growth rate for county i over 14 days and represents the expected change during a fixed unit of time (14 days) 20 5 0 refer to the effects of time varying covariates on the corresponding parameters r 0 is a random effect with mean of 0. All analyses are conducted in the software HLM 7.0 R esults and Discussions Results of Modeling A total of 177 peak events in 16 counties are identified and then analyzed in HLM. At first, an unconditional model with no predictors is tested for each age group to check whether hierarchical modeling is require d and appropriate. Based on the unconditional model, all five age groups are significant ( p <0.05 ), suggesting significant differences between peak events for five age groups. When considering the impacts of time ( DAY ) on the risk of daily ILI cases, however, only two age groups (45 64 and 65+) are significant as shown in Table 4 1. The significant impacts of DAY indicate that there exist significant differences between peak events during a series of 14 days in these t wo age groups Based on the above results, only age groups 45 64 and 65+ can be analyzed in the following analysis. After examining a series of 14 days daily ILI visits from these two age groups in corresponding peak events, results of hierarchical modelin g determine the trajectory of daily ILI vi sits from these two age groups over 14 days during ILI peak events. Tables 4 2 and 4 3 are comparisons between model 1 and model 2 for these two groups. Both models show positive associations between ILI visits and time variable

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73 DAY implying the increasing number of ILI visits with in 14 days The detailed results of associations between variables and daily ILI visits during peak events can be found in Tables B 2 B 5 in Appendix B More importantly, without consider ing the impacts of climate divisions and properties of peak events on daily ILI activity, no meteorological variables are significantly associated with daily ILI activity in peak events. Minimum temperatures and minimum dew points play significant impacts on daily ILI visits from two age groups considering the influences of climate divisions and properties of peak events. Maximum wind speed and average solar radiation have few impacts on the daily number of ILI visits in Florida. However, significant differ ences in effects of properties of peak events on daily ILI visits from these two age groups between counties do emerge Age Among five age groups examined in this study, only two age groups 45 64 and 65+ appear to be significantly represented by an increa sing linear trend of ILI visits over 14 days during peak events. The coefficient of DAY for age group 65+ is 0.024 higher than the coefficient for age group 45 64 as 0.010, suggesting the number of ILI visits from age group 65+ over 14 days increases faste r than ILI visits from age group 45 64. In fact, older people have higher risk of developing severe disease s and death compared with other age groups (Gilca et al., 2011; Zhang et al., 2011; Van Kerkhove et al., 2011). In addition, the lifestyle of aging population in Florida may also contribute to such increasing pattern. Florida has the highest proportion of population 65 years and older in the US. Senior centers and communities with high proportion of older people have high risk of occurrence of flu peaks due to close contact infections. Besides, this study only considers the linear relationship but other non linear relationships may also exist and will be discussed in the future.

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74 Properties of Peak Events Unlike the traditional definition that only captures one single highest ILI peak event per flu year (Smith, 1982; Sakai et al. 2004 ), this study identifies ILI peak events with the definition from the freq uency domain, which is capable of describing the important statistical properties of such peaks, including annual event density, magnitude, and duration. As indicators of county contextual features, the calculated associations between these properties and peak events reveal the initial status (intercept) of daily ILI during peak events in different counties as well as the interplay of these properties and other drivers. Among these three parameters, only parameter for annual event density is significant r elated to daily ILI activity. The coefficient 01 associated with is 0.869 for group 45 64 and 0.534 for group 65+, representing the negative relationship between annual event density and daily ILI activity during peak event Small annual event density results in high number of daily ILI cases at the first day for peak events. This is because a county with small annual event density may experience peak events with remarkable high magnitude (more ILI cases). There is one potent ial limitation of the anal ysis. This study only analyzes 16 most counties did not have the necessary continuity of reports during a longer time period. This does highlight one of the advanta ges of definition of peak event used in this study, which is capable of reasonably maximizing the information from the limited available data for complicated statistical analysis. The added data covering more counties and longer time period in the future can better support the findings in this study. Additi onally, this study only applies the common 80 th percentile as the threshold to define peak events. In practice, t he threshold can be easily extended to other thresholds

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75 of medical interest that are influenced by social, behavioral, and physical factors in the future These extensions can incorporate the impacts of factors on definition that vary in space and then contribute to the surveillance of disease Weather Conditions The significantly negative association between minimum temperature and daily ILI vis its from two age groups indicates daily ILI visits increase when the minimum temperature decreases. The impacts of minimum temperature vary between climate divisions, indicating the occurrence of peak events resulted from geographic variability. For the tw o age groups, the effects of minimum temperature are larger in Divisions 3, 4 and 5 6 than in Division 2. As Lowen et al. (2007) suggested, low temperature increases the transmission rate of various influenza viruses (optimum: 8C). M ean monthly temperatur es ( Figure 4 3 A ) during the coldest month (January) range from the lower 10C in Divisions 1 and 2 to the high 15.6C in Divisions 5 and 6. The sudden drop of temperature in Divisions 3, 4 and 5 may have significant impacts compared with that in Division 2 which is always with relatively low temperature ( K e atinge et al., 1997; K e atinge et al., 2000 ) Independent to temperature changes, dew point is studied in this study as a measure of humidity. Different from the impacts of minimum temperatures, minimum dew point is not significantly associated with daily ILI activity throughout the entire Florida. In fact, Florida is one of the wettest states in the US, approximately on average 1.37 meters of precipitation falling on the State annually ( Winsberg et al., 2003). The Panhandle and southeastern Florida (Divisions 1 and 6) are the two wettest parts of the state ( Figure 4 3 B ). Division 1 experiences two wet seasons, with one in winter, increasing the humidity in the air and decreasing the risk of infection. Due to the amount

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76 of precipitation in the state, there is no significant impact of dew point on ILI peak activity in the entire Florida. However, the interactions of climate divisions and minimum dew points are still estimated. Minimum dew point in Division 4 has a weaker impact on ILI activity for age group 45 64 than that does in Division 2. While for people 65 years and older, minimum dew points in Division 3 and 5 6 have weaker impacts on ILI activity than that does in Division 2. Maximum wind speed and solar radiation do not directly account for the daily ILI activity during peak events in Florida. The maximum wind speed of may play effects on ILI peak events in Florida. The increasing speed of wind results in less risk of ILI peak activity. As Larissa & Christopher (2005) pointed out that substantially more precipitation are associated with faster winds in Pacific inter tropical convergence zone. The increasing amount of precipitation may increase the humidity in the air and then d ecrease the risk of infection. Besides, faster wind can increase air flow and decrease the risk of inhale aerosols with flu virus in the air. In addition to the maximum wind speed, solar radiation is not found to contribute to ILI peak activity in Florida. Belser et al. (2010) suggested that the lack of sunlight in winter aids the survival of the virus in airborne droplets. The low winter UV radiation rates are found to allow aerosolized virus to survive for days in regions of higher latitudes (Sagripanti & Lytle, 2007). Reduced exposure to solar radiation is considered as a determinant of epidemic timing, especially in temperate region (Finkelman et al., 2007; Charland et al., 2009). However, Florida is located at lower sub tropical latitudes which even at winter experiences about 10 hours of daylight and receives about 70% of the solar constant. Such unique feature may minimize the influences of solar radiation on ILI peak activity in Florida

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77 Conclusion s This study presents a two level hierarchical linea r model to spatio temporally measure associations among weather conditions, properties of peak event, and daily ILI activity during peak events in Florida. The identified spatio temporal trends provide statistical evidence of minimum temperature and minimu m dew point as predictors of daily ILI peak activity only for two age groups 45 64 and 65+ in Florida, different from what has been found in the previous studies at weekly or monthly scales. The outcome suggests that minimum temperature is significantly ne gative associated with daily ILI activity for these two age groups throughout the entire Florida. Additionally, the impacts of these predictors vary in climate divisions. The impacts of minimum dew point are larger in the low temperature area than in the r elatively high temperature area. These outcomes would contribute to the current knowledge of influenza diseases in following two folds. First, this study is one of the first attempts to examine the associations between meteorological conditions and ILI act ivity during peak events at a daily scale, which contributes to designing timely effective strategies for disease prevention. More importantly, the identified associations are stratified by age and by climate division, which help to target high risk groups and areas. Second, this study originally incorporates the properties of peak events in analyzing the daily ILI activity in peak events, which has never been discussed. These statistical properties of peak events, derived from historical records describing long term ILI behavior, may help to model ILI peak activity in spatially differentiated areas. From a practical aspect, the peak events defined from the frequency domain allows for the calculation of properties of ILI peak events above the threshold of epidemiological interests. These properties deserve further attention due to their

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78 potential to im prove surveillance and implement intervention strategies by explaining the initial status of daily ILI visits during peak events at spatially differentiated units, for example, the county in this study. Using climate divisions could help to better understa nd the impacts of weather in affecting daily ILI activity during peak events. The associations identified in this study potentially offer a basis for forecasti ng influenza peaks in advance and then help to identify optimal periods and priority regions and risk groups for the implement ations of cost effective influenza vaccination programs. More importantly this model can be appropriately modified for other infectious diseases and easily extended by incorporat ing other covariates such as vaccination rate a nd human mobility

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79 Table 4 1. Parameter estimates for hierarchical modeling with covariate ( DAY ) Age G roup Parameter Coefficient Standard Error P value Confidence Interval 0 4 For DAY slope I ntrcpt 2 ( 10 ) 0.000 0. 003 0. 877 (0.995,1.006) 5 17 For DAY slope I ntrcpt 2 ( 10 ) 0.004 0.003 0. 132 ( 0.990 ,1. 001 ) 18 44 For DAY slope I ntrcpt 2 ( 10 ) 0.003 0. 002 0. 283 (0. 998 ,1. 007 ) 45 64 For DAY slope I ntrcpt 2 ( 10 ) 0.011 0. 004 0 .004** ( 1.004 1.019 ) 65+ For DAY slope I ntrcpt 2 ( 10 ) 0.023 0. 006 0. 000** ( 1.012 1.035 ) ** p <0.01; p <0.05

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80 Table 4 2. Comparisons between model 1 and model 2 for age group 45 64 Model 1 Model 2 Parameter Coefficient P value Coefficient P value For I ntrcpt1 ( 0 ) I ntrcpt 2 ( 00 ) 0.790 0.000 ** 1.031 0. 126 ( 01 ) NA NA 0. 869 0.0 07** k ( 02 ) NA NA 1.166 0.2 04 ( 03 ) NA NA 0.304 0. 671 For DAY slope I ntrcpt 2 ( 10 ) 0.011 0.0 04** 0.01 0 0.0 06** For MINT slope I ntrcpt 2 ( 20 ) 0. 013 0. 181 0.143 0.010* CD 1 ( 21 ) NA NA 0. 028 0. 805 CD 3 ( 22 ) NA NA 0. 156 0. 006** CD 4 ( 23 ) NA NA 0.181 0. 002** CD 5 6 ( 24 ) NA NA 0. 160 0. 005** For MINDP slope I ntrcpt 2 ( 30 ) 0. 010 0 .167 0.085 0.097 CD 1 ( 31 ) NA NA 0. 052 0. 597 CD 3 ( 32 ) NA NA 0.0 95 0. 068 CD 4 ( 33 ) NA NA 0. 117 0 .027* CD 5 6 ( 34 ) NA NA 0.0 92 0. 076 For AVGSR slope I ntrcpt 2 ( 40 ) 0.00 0 0. 365 0.000 0. 329 For MAX WS slope I ntrcpt 2 ( 50 ) 0.0 07 0. 111 0.0 07 0. 086 The value of the likelihood function at iteration 3.575706E+003 3.596112E+003 ** p <0.01; p <0.05

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81 Table 4 3. Comparisons between model 1 and model 2 for age group 65+ Model 1 Model 2 Parameter Coefficient P value Coefficient P value For I ntrcpt1 ( 0 ) I ntrcpt 2 ( 00 ) 1 477 0.000 ** 0.057 0.918 ( 01 ) NA NA 0.534 0.030* k ( 02 ) NA NA 0.880 0.277 ( 03 ) NA NA 0.250 0.688 For DAY slope I ntrcpt 2 ( 10 ) 0.0 23 0.000 ** 0.024 0.000** For MINT slope I ntrcpt 2 ( 20 ) 0. 009 0. 493 0.267 0.001** CD 1 ( 21 ) NA NA 0.134 0.427 CD 3 ( 22 ) NA NA 0.271 0.001** CD 4 ( 23 ) NA NA 0.210 0.010* CD 5 6 ( 24 ) NA NA 0.317 0.000* For MINDP slope I ntrcpt 2 ( 30 ) 0. 001 0. 888 0.146 0.055 CD 1 ( 31 ) NA NA 0.178 0.258 CD 3 ( 32 ) NA NA 0.158 0.040* CD 4 ( 33 ) NA NA 0.111 0.164 CD 5 6 ( 34 ) NA NA 0.170 0.027* For AVGSR slope I ntrcpt 2 ( 40 ) 0.000 0. 949 0.000 0.906 For MAX WS slope I ntrcpt 2 ( 50 ) 0.0 08 0. 208 0.011 0.074 The value of the likelihood function at iteration 3.321069E+003 3.384674E+003 ** p <0.01; p <0.05

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82 Figure 4 1. Climate d ivisions and s tudy counties in Florida

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83 Fig ure 4 2. Definitions of ILI peak events above the 80 th percentile. The insert figure is daily ILI activity in the peak event. 0 10 20 30 40 50 60 70 80 90 100 110 0 5 10 15 20 25 30 35 ILI cases Week The 80 th percentile Data from the ILINet Peak event Epidemc event 0 5 10 15 20 25 0 1 2 3 4 5 6 7 ILI cases Day Data from the ESSENCE

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84 A B Fig ure 4 3 Mean monthly temperature and rainfall in Florida A) M ean monthly temperature, B) M ean monthly precipitation 0 5 10 15 20 25 30 1 2 3 4 5 6 7 8 9 10 11 12 Mean temperature ( C) Month CD1 CD2 CD3 CD4 CD5-6 0 0.05 0.1 0.15 0.2 0.25 1 2 3 4 5 6 7 8 9 10 11 12 Mean rainfall (meter) Month

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85 CHAPTER 5 CONCLUSION As a marker of epidemics, peak event s are one of the most easily identified features, and incorporate a high proportion of the cases in an outbreak ( Charland et al., 2009 ) Their properties, such as annual event density, timing, magnitude and duration, offer critical implicati ons in disease surveillance and control policies. To minimize the impacts of peak events through early prevention and control measures, studies have b een conducted to determine drivers for the outbreak of peak events. T he seasonality of influenza peak s indicates the possible roles of weather in affec ting spread of influenza This research focuses on three study objectives related to peak events: The fir st objective proposes two definitions of peak events and explores the ir statistical properties including annual events density, their timing, magnitude and duration The new definition of events of interests be consider s only, and all, ou tbreaks of epidemiological interest and permit s estimation of the parameters of the distributions, based on commonly encountered thresholds to events above less frequently exceeded thresholds T his approach can be applied to spatially differentiated data a nd determine and compare probabilities associated with influenza events The second objective applies survival analysis to quantify fine scale (daily scale) time lags between weather fluctuations and the onset of ILI peak days throughout Florida. Through defining peak events at three thresholds from the frequency domain, this study finds evidence that the influences of fluctuations of meteorological conditions (minimum temperature, average relative humidity, and minimum dew point ) on ILI peak days vary wi th age (ranging between 3. 1 to 6. 8 days) and over space. The elderly people over 65 years old are the most sensitive to weather fluctuations experiencing

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86 shortest time lags among all age groups while t he age group 18 44 seems to be the least sensitive gro up to weather fluctuations, displaying long est time lags. The identified time lags contribute to improving surveillance and implementing cost effective intervention strategies. The third objective presents a 2 level hierarchical linear model to spatio temp orally measure the association between weather conditions and the likelihood of daily ILI during peak events in Florida. Spatio temporal trends of daily ILI peak activity provide statistical evidence of minimum temperature and minimum dew point as predicto rs of occurrence of peak events. The impacts of these two factors on ILI peak activity also vary in climate divisions These variations suggest that the airborne transmission of influenza virus is enhanced in cold air and low relative humidity, and could improve forecast of peak events at a regional scale. In addition, t his study also reveals a negative relationship between the annual event density and daily ILI visits during peak events which can help to explain the initial status of daily ILI visits during peak events at spatially differentiated areas. Th is research contribute s to the literature on influenza transmission and public health intervention s in the following aspects T his research innovatively applies an established method in hydrology and climatology to the field of epidemiology to describ e the statistical properties of periods during which weekly ILI reports exceed critical thresholds. T he methodology has the added flexibility of being able to extrapolat e influenza peak characteristic s of number and magnitude above various critical thresholds that vary in space and are influenced by social, behavioral, and physical factors. These factors, such as weather conditions, vaccination, and human contact and

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87 mobi lity, are currently the focus of research in the health community The critical thresholds of these factors that contribute to the spread of influenza deserve to be clearly defined in accordance with requirements of surveillance and intervention Additionally, this research is one of the first attempts to examine time lags and the association between meteorological conditions and ILI activity during peak events at a daily scale, which contributes to determining cost effective strategies for disease prevention. It has the ability to forecast peaks at a climate division and daily scale, which minimize the impacts of ecological fallacy and fill the void that only coarse time lags (month ly/weekly lags) are available. More importantly, the identified ass ociations are stratified by age and by climate division, which help to target of high risk groups and areas. Besides this study originally incorporates the properties of peak events in analyzing the daily ILI activity in peak events, which has never been discussed. These statistical properties of peak events are derived from historical records describing long term ILI behavior. The measured impacts of these properties on daily ILI activity in peak events help to improve ILI surveillance and explain the spa tial pattern of ILI peaks. Moreover as one of the earliest studies to utilize the ESSENCE data this research takes advantage of its wide coverage and detailed data to understand ILI activity and associated impacts serv ing as an example of applying ESSEN CE to explore the relationship between disease and environment. Based on the potential and limitations of current studies, future research will mainly focus on exploring the combined impacts of environment and human mobility. The ILI activity are not only resulted from disease and weather interactions, but also from disease and human interactions. Since the influenza spread is highly dependent

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88 on droplets transmission by inhaling the droplets from people with influenza, human contact and mobility plays imp ortant role in the process of transmission. The major sources for human contact and mobility in Florida are through local travel, interstates and air travel. The study of local travel at short distance scale can help to understand the dynamics of influenza spread from inner areas to suburban areas. In addition, the long distance travel through interstates and air travel may bring influenza from north cold States to Florida, and then may spread it to other States or Countries. More impor tantly, the use of pu blic tran spor t may also increase the chance of transmission, due to staying in the limited space without enough fresh air. Besides, as a sunshine State, a number of people prefer to live in Florida after retirement. These new cohort of retirees from other States may br ing influenza to Florida and contribute to influenza transmission in their new communities. These elements associated with human contact and mobility will provide a clear picture of dynamics of influenza transmission in Florida. The spatial network analysi s can be applied to model the dynamics of influenza transmission through travel in the future. In addition app opriate thresholds in Chapter 2 appopriate beginning point of weather fluctuations in Chapter 3 and non linear relationships among weather cond itions daily ILI activity and other statistical properties of peak events in Chapter 4 will be discussed in future studies Finally, future study will increase the diversity of climate divisions and explore the differences of ILI peak activity between sp atially differentiated areas. In conclusion, t he potentially limited information contained in the current definition s of influenza hinders public health professionals from efficiently implementing timing intervention strategies, such as vaccin ation, quarantine, thus

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89 leading to unnecessary socio economic costs. From a practical point of view, based on the definition of peak events, the fine scale time lags and t he associations identified in this research can be used to improve surveillance systems and to determine optimal periods for implementing cost effective influenza vaccination programs among priority high risk groups and areas. Th e approach in this research can be modified appropriately for other inf ectious diseases and easily extended to incorporate other covariates

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90 APPENDIX A SUPPLEMENTARY FIGURE FOR CHAPTER 3 This document shows the supplementary figure used in Chapter 3

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91 Fig ure A 1 Time lags of given age group at three thresholds by meteorological factor by climate division A) Minimum Temp 80%, B ) Minimum Temp 90% C) Minimum Temp 95% D) Average RH 8 0% E ) Average RH 9 0% F ) Average RH 95 % G) Minimum DP 80%, H) Minimum DP 90%, I) Minimum DP 95%. 0 2 4 6 8 10 12 14 0-4 5-17 18-44 45-64 65+ Time lags Age groups A. Minimum Temp 80% CD1 CD2 CD3 CD4 CD5-6 0 2 4 6 8 10 12 14 0-4 5-17 18-44 45-64 65+ Time lags Age groups B. Minimum Temp 90% 0 2 4 6 8 10 12 14 0-4 5-17 18-44 45-64 65+ Time lags Age groups C. Minimum Temp 95% 0 2 4 6 8 10 12 14 0-4 5-17 18-44 45-64 65+ Time lags Age groups D. Average RH 80% 0 2 4 6 8 10 12 14 0-4 5-17 18-44 45-64 65+ Time lags Age groups E. Average RH 90% 0 2 4 6 8 10 12 14 0-4 5-17 18-44 45-64 65+ Time lags Age groups F. Average RH 95% 0 2 4 6 8 10 12 14 0-4 5-17 18-44 45-64 65+ Time lags Age groups G. Minimum DP 80% 0 2 4 6 8 10 12 14 0-4 5-17 18-44 45-64 65+ Time lags Age groups H. Minimum DP 90% 0 2 4 6 8 10 12 0-4 5-17 18-44 45-64 65+ Time lags Age groups I. Minimum DP 95%

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92 APPENDIX B SUPPLEMENTARY TABLE S FOR CHAPTER 4 This document shows the supplementary table s used in Chapter 4 Table B 1. Tim e lags for age groups at the 80 th percentile ( In Days ) Age groups Minimum Temp Average RH Minimum DP 0 4 3. 6 5. 1 3. 6 5 17 3. 8 3. 9 4. 1 18 44 4. 2 4. 6 4.0 45 64 3. 8 4.1 4. 3 65+ 3. 4 4.0 3. 2 Table B 2. Model 1 for age group 45 64: parameter estimates for hierarchical modeling with covariate s Parameter Coefficient Standard Error P value Confidence Interval For I ntrcpt1 ( 0 ) I ntrcpt 2 ( 00 ) 0.790 0. 173 0.000 ** (0.323,0.638) For DAY slope I ntrcpt 2 ( 10 ) 0.011 0.00 3 0.0 04** (1.004,1.019) For MINT slope I ntrcpt 2 ( 20 ) 0. 013 0. 010 0. 181 (0.994,1.032) For MINDP slope I ntrcpt 2 ( 30 ) 0. 010 0. 007 0 .167 (0.977,1.004) For AVGSR slope I ntrcpt 2 ( 40 ) 0.00 0 0.00 0 0. 365 (0.999,1.000) For MAX WS slope I ntrcpt 2 ( 50 ) 0.0 07 0.00 4 0. 111 (0.985,1.002) ** p <0.01; p <0.05

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93 Table B 3. Model 1 for age group 65+: parameter estimates for hierarchical modeling with covariate s Parameter Coefficient Standard Error P value Confidence Interval For I ntrcpt1 ( 0 ) I ntrcpt 2 ( 00 ) 1 477 0. 204 0.000 ** (0.153,0.342) For DAY slope I ntrcpt 2 ( 10 ) 0.0 23 0.00 6 0.000 ** (1.011,1.036) For MINT slope I ntrcpt 2 ( 20 ) 0. 009 0. 014 0. 493 (0.964,1.018) For MINDP slope I ntrcpt 2 ( 30 ) 0. 001 0. 010 0. 888 (0.982,1.022) For AVGSR slope I ntrcpt 2 ( 40 ) 0.000 0.00 0 0. 949 (0.999, 1.001) For MAX WS slope I ntrcpt 2 ( 50 ) 0.0 08 0.00 6 0. 208 (0.981,1.004) ** p <0.01; p <0.05

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94 Table B 4. Model 2 for age group 45 64: parameter estimates for hierarchical modeling with covariate s Parameter Coefficient Standard Error P value Confidence Interval For I ntrcpt1 ( 0 ) I ntrcpt 2 ( 00 ) 1.031 0. 670 0. 126 (0.748, 10.502) ( 01 ) 0. 869 0. 316 0.0 07** (0.225, 0.782) k ( 02 ) 1.166 0. 91 3 0.2 04 (0.052, 1.884) ( 03 ) 0.304 0. 716 0. 671 (0.180, 3.023) For DAY slope I ntrcpt 2 ( 10 ) 0.01 0 0.00 4 0.0 06** (1.003, 1.019) For MINT slope I ntrcpt 2 ( 20 ) 0.143 0.055 0.010* (0.778, 0.966) CD 1 ( 21 ) 0. 028 0.1 13 0. 805 (0.825, 1.282) CD 3 ( 22 ) 0. 156 0.0 56 0. 006** (1.046, 1.306) CD 4 ( 23 ) 0.181 0.0 58 0. 002** (1.070, 1.343) CD 5 6 ( 24 ) 0. 160 0.0 57 0. 005** (1.050, 1.312) For MINDP slope I ntrcpt 2 ( 30 ) 0.085 0.051 0.097 (0.985, 1.203) CD 1 ( 31 ) 0. 052 0. 098 0. 597 (0.869, 1.276) CD 3 ( 32 ) 0.0 95 0.0 52 0. 068 (0.821, 1.007) CD 4 ( 33 ) 0. 117 0.0 53 0 .027* (0.801, 0.987) CD 5 6 ( 34 ) 0.0 92 0.0 52 0. 076 (0.823, 1.010) For AVGSR slope I ntrcpt 2 ( 40 ) 0.000 0.000 0. 329 (0.999, 1.000) For MAX WS slope I ntrcpt 2 ( 50 ) 0.0 07 0.00 4 0. 086 (0.984, 1.001) ** p <0.01; p < 0.05

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95 Table B 5. Model 2 for age group 65+: parameter estimates for hierarchical modeling with covariate s Parameter Coefficient Standard Error P value Confidence Interval For I ntrcpt1 ( 0 ) I ntrcpt 2 ( 00 ) 0.057 0.543 0.918 (0.324, 2.756) ( 01 ) 0.534 0.245 0.030* (0.362, 0.950) k ( 02 ) 0.880 0.805 0.277 (0.085, 2.028) ( 03 ) 0.250 0.622 0.688 (0.229, 2.653) For DAY slope I ntrcpt 2 ( 10 ) 0.024 0.006 0.000** (1.011, 1.037) For MINT slope I ntrcpt 2 ( 20 ) 0.267 0.077 0.001** (0.658, 0.891) CD 1 ( 21 ) 0.134 0.168 0.427 (0.629, 1.217) CD 3 ( 22 ) 0.271 0.078 0.001** (1.126, 1.528) CD 4 ( 23 ) 0.210 0.081 0.010* (1.053, 1.445) CD 5 6 ( 24 ) 0.317 0.077 0.000* (1.180, 1.598) For MINDP slope I ntrcpt 2 ( 30 ) 0.146 0.076 0.055 (0.997, 1.343) CD 1 ( 31 ) 0.178 0.157 0.258 (0.878, 1.625) CD 3 ( 32 ) 0.158 0.077 0.040* (0.735, 0.993) CD 4 ( 33 ) 0.111 0.079 0.164 (0.766, 1.046) CD 5 6 ( 34 ) 0.170 0.077 0.027* (0.725, 0.981) For AVGSR slope I ntrcpt 2 ( 40 ) 0.000 0.001 0.906 (0.999, 1.001) For MAX WS slope I ntrcpt 2 ( 50 ) 0.011 0.006 0.074 (0.978, 1.001) ** p <0.01; p <0.05

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96 LIST OF REFERENCES Aditama TY Samaan G Kusriastuti R Purba WH Misriyah Santoso H et al. Risk factor s for cluster outbreaks of avian influenza A H5N1 infection, Indonesia. Clin Infect Dis 2 011 ; 53(12):1237 44. Alonso WJ, Viboud C, Simonsen L, Hirano EW, Daufenbach LZ, Miller MA Seasonality of influenza in Brazil : a traveling wave from the Amazon to the subtropics. American Journal of Epidemiology 2007 ; 165 (12) : 14341442. Bock D Andersson E Frisn M Statistical surveillance of epidemics: peak detection of influenza in Sweden. Biom J 2008 ; 50(1) : 71 85. Belser JA, Maines TR, Tumpey TM, Katz JM Influenza A virus transmission: contributing factors and clinical implications. Expert Reviews in Molecular Medicine 2010 ; 12: e39. Bryk AS, Raudenbush SW Application of hierarchical linear models to assessing change. Psychological Bulletin 1987 ; 101(1): 147 158. Cannell JJ, Vieth R, Umhau JC, Holick MF, Grant WB, Madronich S, et al. Epidemic influenza and vitamin D. Epidemiology and Infection 2006 ; 134(6): 112 9 1140. Centers for Disease Control and Prevention. Available from http :// www cdc gov / flu / keyfacts htm ; 2012 Chan T C, King C C, Yen M Y, Chiang P H, Huang C S, Chuhsing K H. Probabilistic Daily ILI Syndromic Surveillance with a Spatio Temporal Bayesian Hierarchical Model. PLoS ONE 2010;5(7):e11626. Charland KML, Buckeridge DL Sturtevant JL Melton F, Brownstein JS Does Climate Predict the Timing of Peak Influenza Activity in the United States? Advances in Disease Surveillance 2008; 5( 3 ) : 169. Charland KML, Buckeridge DL Sturtevant JL Melton F, Reis BY, Mandl KD, et al. Effect of environment al factors on the spatio temporal patterns of influenza spread. Epidemiol Infect 2009; 137(10) : 1377 87. Chowell G, Bertozzi SM, Colchero MA, Lopez Gatell H, Alpuche Aranda C, Hernandez M, et al. Severe Respiratory Disease Concurrent with the Circulation of H1N1 Influenza. N Engl J Med ; 361(7) : 674 679. Cooley P, Ganapathi L Ghneim G, Holmberg S, Wheaton W, Hollingsworth CR Using influenza like illness data to reconstruct an influenza outbreak. Mathematical and Computer Modelling 2008 ; 48 (5 6): 929 939.

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97 Cooper DL Verlander NQ Elliot AJ Joseph CA Smith GE Can syndromic thresholds provide early warning of national influenza outbreaks? J Public Health 2009; 31 (1) : 17 25. Cowling BJ, Wong IO, Ho LM, Riley S, Leung GM. Methods for monitoring influenza surveillance dat a. Int J Epidemiol 2006;35(5): 1314 1321. Cramer H, Leadbetter MR Stationary and related stochastic processes. New York : Wiley ; 1967. D avis RE, Rossier CE, Enfield KB. The Impact of Weather on Influenz a and Pneumonia Mortality in New York City, 1975 2002: A Retrospective Study. PLoS ONE 2012 ; 7(3): e34091. Desmond AF, Guy BT. Crossing Theory for Non Gaussian Processes With an Application to Hydrology. Water Resources Research 1991;279(10): 2791 2797. Ertek M, Durmaz R, Guldemir D, Altas AB Albayrak N Korukluoglu G Epidemiological, Demographic, and Molecular Characteristics of Laboratory Confirmed Pandemic Influenza A (H1N1) Virus Infection in Turkey Jpn J Infect D is 2010; 63 (5): 239 245. ESSENCE User Guide Florida Department of Health Bureau of Epidemiology Avaliable from http://www.doh.state.fl.us/disease_ctrl/epi/Acute/Florida_ESSENCE_user_guide.pdf ; 2010 Fang LQ, de Vlas SJ, Lian g S, Looman CWN, Gong P, Xu B, e t al Environmental Factors Contributing to the Spread of H5N1 Avian Influenza in Mainland China. PLoS ONE 2008 ; 3(5) : e2268. Finkelman BS, Viboud C, Koelle K, Ferrari MJ, Bharti N, Grenfell BT Global Patterns in Seasonal Activity of Influenza A/H3N2, A/H1N1, and B from 1997 to 2005: Viral Coexistence and Latitudinal Gradients. PLoS ONE 2007 ; 2(12): e1296. Fleming DM Zambon M Bartelds AIM, de Jong JC. The duration and magnitude of influenza epidemics: A study of surveillance data from sentinel general practices in England, Wales and the Netherlands European Journal of Epidemiology 1999; 15(5): 467 473. Florida Department of Health. Available from http://www.doh.state.fl.us/disease_ctrl/epi/htopics/flu/FSPISN /influenza_sentinels.h tml ; 2012 a Florida Department of Health. Available from http://www.doh.state.fl.us/disease_ctrl/epi/htopics/flu/panflu.htm ; 2012b Florida Department of Health Available from http://www.doh.state.fl.us/floridaflu/FSPISN/influenza_sentinels.html ; 2012c

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101 Yassine HM Lee CW Gourapura R Saif YM Interspecies and intraspecies transmission of influenza A viruses: viral, host and environmental factors. Anim Health Res Rev 2010 ; 11 (1): 53 72. Zar aket H Saito R Tanabe N Taniguchi K Suzuki H Association of early annual peak influenza activity with El Nio southern oscillation in Japan. Influenza Other Respi Viruses 2008 ; 2(4) : 12 30. Zhang AJ, To KK, Tse H, Chan KH, Guo KY, Li C, et al. High incidence of severe influenza among individuals aged over 50 years. Clin Vaccine Immunol 2011 ; 18(11):1918 24.

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102 BIOGRAPHICAL SKETCH Ying Wang was born and grew up in Wuhan, China In June 2006, she received a Bach elor of Science in Geographic Information System (GIS) of the School of Resource and Environment al Science from Wuhan University, China. Then in June 2008, Ying received a Master of Science in Cartography and GIS of the School of Resource and Environment al Science from Wuhan University, China. Ying began her doctorate program in G eography at the University of Florida in August 2008. She focused on numerical methods in public health and spatial epidemiology. Her dissertation was on s patio temporal modeling f or peak events of seasonal influenza in Florida


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