Mathematical and Statistical Modeling for Emerging and Re emerging Infectious Diseases 1st Edition by Gerardo Chowell, James Hyman 3319404134 9783319404134

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ISBN-10 :  3319404134 

ISBN-13 :  9783319404134

Author: Gerardo Chowell,  James M. Hyman 

  The contributions by epidemic modeling experts describe how mathematical models and statistical forecasting are created to capture the most important aspects of an emerging epidemic.Readers will discover a broad range of approaches to address questions, such as Can we control Ebola via ring vaccination strategies? How quickly should we detect Ebola cases to ensure epidemic control?  What is the likelihood that an Ebola epidemic in West Africa leads to secondary outbreaks in other parts of the world?   When does it matter to incorporate the role of disease-induced mortality on epidemic models?  What is the role of behavior changes on Ebola dynamics?  How can we better understand the control of cholera or Ebola using optimal control theory? How should a population be structured in order to mimic the transmission dynamics of diseases such as chlamydia, Ebola, or cholera? How can we objectively determine the end of an epidemic? How can we use metapopulation models to understand the role of movement restrictions and migration patterns on the spread of infectious diseases? How can we capture the impact of household transmission using compartmental epidemic models? How could behavior-dependent vaccination affect the dynamical outcomes of epidemic models?  The derivation and analysis of the mathematical models addressing these questions provides a wide-ranging overview of the new approaches being created to better forecast and mitigate emerging epidemics.  This book will be of interest to researchers in the field of mathematical epidemiology, as well as public health workers.

Mathematical and Statistical Modeling for Emerging and Re emerging Infectious Diseases 1st Table of contents:

Modeling the Impact of Behavior Change on the Spread of Ebola
1 Introduction
2 Mathematical Model
2.1 Rates of Infection
2.2 Progression Rates
2.3 Behavior Change, Healthcare Availability, and Traditional Funerals
3 Reproduction Numbers
3.1 Branching Process Derivation of the Reproductive Numbers
3.2 Next Generation Method Derivation of the Basic Reproductive Number
4 Parameter Estimation from Montserrado EVD Cases
5 Sensitivity Analysis
6 Summary and Conclusions
References
A Model for Coupled Outbreaks Contained by Behavior Change
1 Introduction
2 Final Size of a Single Outbreak with Behavior Change
3 Global Epidemic Model
4 Comparison with Numerical Results
5 Discussion
References
Real-Time Assessment of the International Spreading Risk Associated with the 2014 West African Ebola
1 Introduction
2 Methods
2.1 Global Epidemic and Mobility Model
2.2 Disease Dynamic Model
2.3 Real-Time Model Calibration
2.4 Containment Scenarios
3 Results
3.1 Local Transmission of EVD
3.2 Assessing the International Spread of EVD
4 Discussion
References
Modeling the Case of Early Detection of Ebola Virus Disease
1 Introduction
2 Model Formulation
3 Model Analysis
3.1 Basic Properties
3.2 Equilibrium Analysis
3.3 Normalized Sensitivity Analysis on mathcalRc
3.4 Impact of Early Detection and Isolation on the Value of mathcalRc
4 Discussion and Conclusion
References
Modeling Ring-Vaccination Strategies to Control Ebola Virus Disease Epidemics
1 Introduction
2 Methods
3 Household-Community Structure
4 SEIR-SV Transmission
5 Homogeneous and Heterogeneous Transmission Rates on the Network
6 Parameter Values, Initial Conditions for Simulations and Details of a Simulated Vaccination Progr
7 Results
7.1 Even Without Vaccination, Outbreaks Have a High Probability of Spontaneously Extinguishing Early
7.2 Earlier Vaccination of Infected Individuals Increases the Probability that Outbreaks Will Extin
8 Discussion
References
Evaluating the Number of Sickbeds During Ebola Epidemics Using Optimal Control Theory
1 Introduction
2 Materials and Method
2.1 Mathematical Model of EVD Transmission
2.2 Optimal Control Strategy for Prevention of EVD
2.3 Characteristics of Optimal Control
3 Results and Discussion
3.1 Optimal Control Strategies for Various Weight Constants
3.2 Estimation of the Maximum Number of Sickbeds
References
Inverse Problems and Ebola Virus Disease Using an Age of Infection Model
1 Introduction
2 Ill-Posedness of the Least Squares Problem
3 Computation of Initial Values
4 Regularization Algorithm and Experimental Results for Simulated Data
5 Numerical Analysis for Real Data
6 Discussion and Future Plans
References
Assessing the Efficiency of Movement Restriction as a Control Strategy of Ebola
1 Introduction
2 Prior Modeling Work
3 The Model Derivation
4 EDV Dynamics in Heterogeneous Risk Environments
4.1 Formulation of the Model
4.2 Final Epidemic Size in Heterogeneous Risk Environments
5 Simulations
5.1 One Way Mobility
5.2 Symmetric Mobility
5.3 Final Size Analysis
5.4 Final Size and Basic Reproductive Number Analysis
6 Conclusion
References
Patch Models of EVD Transmission Dynamics
1 Introduction
2 Modeling Methods
2.1 Logistic Equation as an Ebola Cumulative Infections Case Model
2.2 Derivation of R0 and Re
2.3 Incorporating Population Heterogeneity: Multi-patch Models
3 Comparison Methods
3.1 Ranking Models by Fitting and Forecasting Errors
3.2 Parameters and Confidence Interval Assessment
3.3 Challenges
4 Results
4.1 Data Based Model Validation
4.2 Forecasting Error as a Function of Forecasting Points
4.3 Confidence Interval Assessment
4.4 Implications for Liberia, Sierra Leone and Guinea: R0
5 Discussion
References
From Bee Species Aggregation to Models of Disease Avoidance: The Ben-Hur effect
1 Introduction
2 Phenomenological Model
3 Cross-Diffusion Models
3.1 SI Model with Diffusion
3.2 Effects of Recruitment
3.3 Effects of Incidence Functions
3.4 Necessary and Sufficient Conditions
4 Discussion and Conclusion
References
Designing Public Health Policies to Mitigate the Adverse Consequences of Rural-Urban Migration via M
1 Introduction
2 Models and Analysis
2.1 The Long-Term Endemic Model
2.2 The Short-Term Model
2.3 Stochastic Simulations of the Short-Term Model
3 Impact of Vaccination Policies on Short-Term Outbreaks
4 Discussion
References
Age of Infection Epidemic Models
1 Introduction
2 The Modern Infection Age Epidemic Model
3 Example: The General SEIR Model
4 A Heterogeneous Mixing Age of Infection Model
5 The Invasion Criterion
6 The Final Size of a Heterogeneous Mixing Epidemic
7 Conclusions
References
Optimal Control of Vaccination in an Age-Structured Cholera Model
1 Introduction
2 The Model and Optimal Control Formulation
3 Existence of the Solution to the State System
4 Conditions for Optimality
5 Existence of the Optimal Control
6 Parameter Choices
6.1 Proportion of Symptomatic Infections p
6.2 Transmission Rates βL and βH
6.3 Waning Immunity
6.4 Death Rates
6.5 Michaelis Constants κL and κH
6.6 Shedding Rates η1 and η2
6.7 Vibrio Rates
6.8 Maximum Daily Vaccination Rate
7 Numerical Results
8 Conclusions
References
A Multi-risk Model for Understanding the Spread of Chlamydia
1 Introduction
2 Mathematical Model
2.1 Migration Rate
2.2 Disease Recovery Rate
2.3 Disease Transmission Rate
3 Basic Reproduction Number
3.1 Branching Process Analysis
3.2 Next Generation Derivation of Basic Reproduction Number
4 Sensitivity Analysis
4.1 Sensitivity Indices of mathbbR0
4.2 Sensitivity Indices of Endemic Equilibriums
5 Numerical Simulations
6 Summary and Conclusions
References
The 1997 Measles Outbreak in Metropolitan São Paulo, Brazil: Strategic Implications of Increasing
1 Introduction
1.1 Background
1.2 Outbreak Control in São Paulo
2 Methods
2.1 Descriptive Modeling
2.2 Mechanistic Modeling
2.3 Parameters and Initial Conditions
2.4 Experimental Design
3 Results
3.1 Descriptive Epidemiology
3.2 Mechanistic Modeling
4 Discussion
4.1 Policy Implications
4.2 Reflections
4.3 Further Modeling
References
Methods to Determine the End of an Infectious Disease Epidemic: A Short Review
1 Prologue
2 Classical WHO Approach
3 Single Exposure Approach
4 Laboratory Testing to Ensure the Absence of Cases
5 An Explicit Method for Multiple Exposure Setting
6 A Heuristic Method for Multiple Exposure Setting
7 Conclusions
References
Statistical Considerations in Infectious Disease Randomized Controlled Trials
1 Introduction
2 Modern Statistical Analysis of RCT Data
3 Sample Size Determination
4 Data Monitoring, Interim, and Subgroup Analyses
5 Multisite and Cluster Randomized Trials
6 Discussion
References
Epidemic Models With and Without Mortality: When Does It Matter?
1 An Agent-Based Influenza Model with Mortality
1.1 Set-up of the Population
1.2 Daily Activities Incorporated into the Model
1.3 The Disease Transmission Process
2 Analysis of the Model
2.1 General Effects of Adding Mortality to an Epidemic Model
2.2 The Effect of Mortality on Ultimate Numbers of Cases and Proportions of a Population Affected by
2.3 Models with Mortality and the Development of Oscillations in the Numbers of Infected Individual
3 Discussion
References
Capturing Household Transmission in Compartmental Models of Infectious Disease
1 Introduction
2 Compartmental Model
3 Epidemic Simulation and Probabilistic Contact Matrices
4 Results
5 Discussion
6 Conclusion
References
Bistable Endemic States in a Susceptible-Infectious-Susceptible Model with Behavior-Dependent Vacc
1 Introduction
2 The SISV Model with Prevalence-Dependent Vaccine Uptake and Its Disease-Free Equilibrium
3 Instability of the Disease-Free State: Mono Versus Multistability
3.1 Bistable Endemicity Induced by a Linear-Saturated Vaccine Uptake p(I)
4 Local Stability of the Disease-Free: Global Stability Versus Backward Bifurcations
5 Concluding Remarks

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