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Table of Contents
Preface; Contents; List of Symbols; Part I Mathematical Background; 1 Basic Theory; 1.1 Preliminaries; 1.2 Ordinary Differential Equations; 1.2.1 Fundamental Theory; 1.2.2 Stability Theory; 1.2.3 Partial Stability; 1.3 Impulsive Systems; 1.4 Delay Differential Equations; 1.5 Stochastic Differential Equations; 2 Hybrid and Switched Systems; 2.1 Stability Under Arbitrary Switching; 2.2 Stability Under Constrained Switching; 2.3 Switching Control; Part II Hybrid Infectious Disease Models; 3 The Switched SIR Model; 3.1 Model Formulation; 3.2 Threshold Criteria: The Basic Reproduction Number.
3.3 Seasonal Variations in Disease Transmission: Term-Time Forcing3.4 Adding Population Dynamics: The Classical Endemic Model; 3.5 Generalizing the Incidence Rate of New Infections; 3.6 Uncertainty in the Model: Stochastic Transmission; 3.7 Discussions; 4 Epidemic Models with Switching; 4.1 Absence of Conferred Natural Immunity: The SIS Model; 4.2 Multi-City Epidemics: Modeling Traveling Infections; 4.3 Vector-Borne Diseases with Seasonality; 4.4 Other Epidemiological Considerations; 4.4.1 Vertical Transmission; 4.4.2 Disease-Induced Mortality: Varying Population Size.
4.4.3 Waning Immunity: The Switched SIRS Model4.4.4 Passive Immunity: The Switched MSIR Model; 4.4.5 Infectious Disease Model with General Compartments; 4.4.6 Summary of Mode Basic Reproduction Numbers and Eradication Results; 4.5 Discussions; Part III Control Strategies; 5 Switching Control Strategies; 5.1 Vaccination of the Susceptible Group; 5.2 Treatment Schedules for Classes of Infected; 5.3 Introduction of the Exposed: A Controlled SEIR Model; 5.4 Screening of Traveling Individuals; 5.5 Switching Control for Vector-borne Diseases; 5.6 Discussions; 6 Pulse Control Strategies.
6.1 Public Immunization Campaigns: Control by Pulse Vaccination and Treatment6.1.1 Impulsive Control Applied to the Classical Endemic Model; 6.1.2 Incorporating Impulsive Treatment into the Public Campaigns; 6.1.3 The SIR Model with General Switched Incidence Rates; 6.1.4 Vaccine Failures; 6.1.5 Pulse Control Applied to an Epidemic Model with Media Coverage; 6.1.6 Multi-City Vaccination Efforts; 6.1.7 Pulse Vaccination Strategies for a Vector-Borne Disease; 6.2 Discussions; 6.2.1 Comparison of Control Schemes; 7 A Case Study: Chikungunya Outbreakin Réunion; 7.1 Background.
7.2 Human-Mosquito Interaction Mechanisms7.3 Chikungunya Virus Model Dynamics; 7.4 Control via Mechanical Destruction of Breeding Grounds; 7.5 Control via Reduction in Contact Rate Patterns; 7.6 Control Analysis: Efficacy Ratings; 7.6.1 Assessment of Mechanical Destruction of Breeding Sites; 7.6.2 Assessment of Reduction in Contact Rate Patterns; 7.7 Discussions; Part IV Conclusions and Future Work; 8 Conclusions and Future Directions; References.
3.3 Seasonal Variations in Disease Transmission: Term-Time Forcing3.4 Adding Population Dynamics: The Classical Endemic Model; 3.5 Generalizing the Incidence Rate of New Infections; 3.6 Uncertainty in the Model: Stochastic Transmission; 3.7 Discussions; 4 Epidemic Models with Switching; 4.1 Absence of Conferred Natural Immunity: The SIS Model; 4.2 Multi-City Epidemics: Modeling Traveling Infections; 4.3 Vector-Borne Diseases with Seasonality; 4.4 Other Epidemiological Considerations; 4.4.1 Vertical Transmission; 4.4.2 Disease-Induced Mortality: Varying Population Size.
4.4.3 Waning Immunity: The Switched SIRS Model4.4.4 Passive Immunity: The Switched MSIR Model; 4.4.5 Infectious Disease Model with General Compartments; 4.4.6 Summary of Mode Basic Reproduction Numbers and Eradication Results; 4.5 Discussions; Part III Control Strategies; 5 Switching Control Strategies; 5.1 Vaccination of the Susceptible Group; 5.2 Treatment Schedules for Classes of Infected; 5.3 Introduction of the Exposed: A Controlled SEIR Model; 5.4 Screening of Traveling Individuals; 5.5 Switching Control for Vector-borne Diseases; 5.6 Discussions; 6 Pulse Control Strategies.
6.1 Public Immunization Campaigns: Control by Pulse Vaccination and Treatment6.1.1 Impulsive Control Applied to the Classical Endemic Model; 6.1.2 Incorporating Impulsive Treatment into the Public Campaigns; 6.1.3 The SIR Model with General Switched Incidence Rates; 6.1.4 Vaccine Failures; 6.1.5 Pulse Control Applied to an Epidemic Model with Media Coverage; 6.1.6 Multi-City Vaccination Efforts; 6.1.7 Pulse Vaccination Strategies for a Vector-Borne Disease; 6.2 Discussions; 6.2.1 Comparison of Control Schemes; 7 A Case Study: Chikungunya Outbreakin Réunion; 7.1 Background.
7.2 Human-Mosquito Interaction Mechanisms7.3 Chikungunya Virus Model Dynamics; 7.4 Control via Mechanical Destruction of Breeding Grounds; 7.5 Control via Reduction in Contact Rate Patterns; 7.6 Control Analysis: Efficacy Ratings; 7.6.1 Assessment of Mechanical Destruction of Breeding Sites; 7.6.2 Assessment of Reduction in Contact Rate Patterns; 7.7 Discussions; Part IV Conclusions and Future Work; 8 Conclusions and Future Directions; References.