List of Figures. 3.1 Endsley s Model of Situational Awareness Endsley s Model Applied to Biosurveillance... 64

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1 List of Figures 1.1 Select Worldwide Disease Occurrences in Recent Decades Biosurveillance Taxonomy Public Health Surveillance Taxonomy Improving the Probability of Detection Using Biosurveillance Biosurveillance System Data Flow BioSense Data Display Google Flu Trends Plot HealthMap Screen Shot Snow s Map of the 1854 London Cholera Epidemic Types of Data Map of Over-the-Counter Thermometer Sales from RODS Comparison of Employee Absenteeism to Syndromic Surveillance Indicators One Year of Gastrointestinal Syndrome Data for Clinics One Year of Influenza-like Illness Syndrome Data for Clinics Average Day Effect for ILI and Gastrointestinal Syndrome Data from the Clinics Smoothed Counts of Gastrointestinal Syndrome for Seven Hospitals Smoothed Counts of Respiratory Syndrome for Seven Hospitals Average Day Effect for Respiratory Syndrome Data for the Seven Hospitals Steps in Data Preparation Endsley s Model of Situational Awareness Endsley s Model Applied to Biosurveillance... 64

2 XVIII List of Figures 3.3 Situational Awareness Levels with Associated Information Requirements Shattuck and Miller s Dynamic Model of Situated Cognition Correlogram for Clinic Gastrointestinal Syndrome Data Correlogram for Clinic ILI Syndrome Data Bar Charts of Clinic Demographics Stacked Bar Chart of Clinic Demographics Side-by-Side Bar Chart of Clinic Demographics Histogram of Clinic Patient Age Data Histogram of Transformed Clinic Age Data Histogram Variants Lattice Plot of Respiratory Data by Hospital Lattice Plot of Clinic Patient Age Histograms by Gender and Ethnicity How a Box Plot is Constructed Box Plot of Clinic Patient Age Data Side-by-side Box Plots of Clinic Patient Ages by Ethnicity Scatterplot of Hospital #1 Versus Hospital #2 Respiratory Syndrome Daily Count Data Scatterplot of Clinic GI Versus ILI Daily Count Data Scatterplot Matrix of Hospital Respiratory Data Time Series Plot Variants Repeated Box Plots for Longitudinal Data Plot of Repeated Box Plot Statistics Lattice Plot for Longitudinal Data Map of Clinic Population Density by ZIP Code Map of Clinic Annual ILI Counts by ZIP Code Maps of the Weekly ILI Rate for the Clinic Data Weekly ILI Maps Showing Percent Increase Over Baseline Rate Bubble Chart of Clinic Population Density by ZIP Code Correlogram for Clinic Gastrointestinal Syndrome Residuals Correlogram for Clinic ILI Syndrome Residuals Holt-Winters Model and Forecast for Clinic GI Data Moving Averages for Hospital #7 GI Data Moving Averages for the Last Year of Hospital #7 GI Data Moving Average 30-Day Forecast of Hospital #7 GI Data...132

3 List of Figures XIX 5.7 Exponentially Weighted Moving Average Forecasts for Hospital #7 GI Data Plot of MSE Versus λ for Exponentially Weighted Moving Average Forecasts Exponentially Weighted Moving Average Model with λ = 0.16 for Hospital #7 GI Data with 90-Day Forecast Holt Double Exponential Model with λ = 0.2 and γ = 0.06 for Hospital #7 GI Data with 90-Day Forecast Holt-Winters Triple Exponential Model with s = 7 for Hospital #7 GI Data with 90-Day Forecast Holt-Winters Triple Exponential Model with s = 365 for Hospital #7 GI Data with 90-Day Forecast Simple Linear Regression Line Fit to Hypothetical Data Autoregression Model with p = 8 for Hospital #7 GI Data with 90-Day Forecast Adaptive Regression Used to Predict Day 980 of the Hospital GI Data Adaptive Regression Used to Predict the Last Month of the Hospital GI Data Adaptive Regression Forecasts Using n = 56 for Hospital #7 Data Optimal Adaptive Regression Forecasts Using n = 30 for Hospital #7 Data Change Point Analysis Applied to the Hospital #7 GI Data Binary Classification Test Outcomes Test Measure Distributions for Two Populations: Sick and Healthy Illustrating a Receiver Operating Characteristic (ROC) Curve Hypothetical Sampling Distributions An Illustrative Hypothesis Test ROC Curve A Sequential Probability Ratio Test (SPRT) Plot Example Figure I from Notifiable Diseases/Deaths in Selected Cities Weekly Information A Plot of the Shewhart Method Simulated Gastrointestinal Chief Complaint Data Probability Mass Function for a Poisson Distribution with λ = ATFS, CED, and PSD Graphs for Example A Plot of the CUSUM Method Applied to ILI Syndrome Residuals...212

4 XX List of Figures 7.7 Plot of CUSUM Statistics for Example CED and PSD Plots for Example CED and PSD Plots for Example A Plot of the EWMA Method Applied to ILI Syndrome Residuals CED and PSD Plots for Example Plot of EWMA Statistics for Example CED and PSD Plots for Example CED and PSD Plots for Example Contours of a Bivariate Normal Distribution for Various CorrelationValues Detection Regions for Hotelling s χ 2 Detection Method Modified for Biosurveillance Illustrating the MCUSUM Calculations Plot of Hospital #7 GI Data Plot of Hospital #7 GI Data with Signal Times Plot of Hospital #7 GI Data for Select Days Plot of Hospital #7 GI Sata with Signal Times CUSUM Signals for the Hospital #7 GI Data Plot of Hospital #2 Data Plot of Hospital #2 Data with Signal Times Plot of Clinic ILI Data with Signal Times Plots of Hospital #7 GI Syndrome Data Plots of Adaptive Regression Residuals Plot of Hospital #7 Data with EED Signal Times Plot of Estimated λ Values Plot of Hospital #2 Data with EED Signal Times Percentage of Patients Classified with ILI Comparison of Estimated ILI Counts EED Signal Times for Baseline ILI Definition EED Signal Times for Expanded ILI Definition EED Signal Times for Restricted ILI Definition Example of Simulated Data Average Squared Residuals for Linear and Quadratic Models Performance of the Methods for Scenario Performance of the Methods for Scenario

5 List of Figures XXI 10.5 Performance Comparison of the CUSUM versus Shewhart Method Comparison of the MCUSUM for Various k to the MEWMA with λ = Performance of the MCUSUM and MEWMA for Scenario Performance of the MEWMA and MCUSUM A.1 Venn Diagram of Disjoint Events A.2 Venn Diagram of Complementary Events A.3 Venn Diagrams of Union and Intersection of Events A.4 Various Binomial Probability Mass Functions A.5 Various Poisson Probability Mass Functions A.6 Various Negative Binomial Probability Mass Functions A.7 Probability Density Function for Uniform Distribution A.8 Probability Density Function for Standard Normal Distribution 352 A.9 Comparing Probability Density Functions for N(0,1) vs. N(0,2). 353 A.10 Various t Distribution Probability Density Functions A.11 Illustrative Chi-square Probability Density Functions A.12 Illustrative F Distribution Probability Density Functions A.13 Central Limit Theorem Illustration B.1 Distribution of ILI Syndrome Counts for the Clinic Data B.2 Distribution of GI Syndrome Counts for the Clinic Data B.3 Q-Q Plots of ILI and Gastrointestinal Syndrome Residuals for the Clinic Data B.4 Illustration of UTM1 Systematic Effects B.5 Hospital #7 Actual vs. Simulated Gastrointestinal Syndrome Data B.6 Hospital #7 Actual vs. Simulated Respiratory Syndrome Data. 373 B.7 Hospital #7 Simulated Gastrointestinal Syndrome Data B.8 Hospital #7 Actual vs. Simulated Respiratory Syndrome Data. 375 B.9 Two Years of Hospital #7 GI Data B.10 Actual Hospital #7 GI Data Compared to Simulated Data B.11 Plot of Jump Change Outbreak Form B.12 Plot of triangular Outbreak Form B.13 Plot of a More Complicated Outbreak Form B.14 Multivariate Simulation Results B.15 Multivariate Simulation Results B.16 Multivariate Simulation Results Compared to Actual Data...390

6 XXII List of Figures B.17 Spatio-temporal Biosurveillance Simulation Flowchart...392