| Description |
1 online resource (xvi, 271 pages) : illustrations (some color) |
| Series |
Nonlinear systems and complexity, 2195-9994 ; volume 19 |
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Nonlinear systems and complexity ; v. 19.
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| 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 |
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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 |
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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 |
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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 |
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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 |
| Summary |
This volume presents infectious diseases modeled mathematically, taking seasonality and changes in population behavior into account, using a switched and hybrid systems framework. The scope of coverage includes background on mathematical epidemiology, including classical formulations and results; a motivation for seasonal effects and changes in population behavior, an investigation into term-time forced epidemic models with switching parameters, and a detailed account of several different control strategies. The main goal is to study these models theoretically and to establish conditions under which eradication or persistence of the disease is guaranteed. In doing so, the long-term behavior of the models is determined through mathematical techniques from switched systems theory. Numerical simulations are also given to augment and illustrate the theoretical results and to help study the efficacy of the control schemes |
| Bibliography |
Includes bibliographical references |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed March 7, 2017) |
| Subject |
Communicable diseases -- Mathematical models
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Communicable diseases -- Epidemiology
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Infectious & contagious diseases.
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Cybernetics & systems theory.
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Nonlinear science.
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Epidemiology & medical statistics.
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Mathematical modelling.
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MEDICAL -- Infectious Diseases.
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Communicable diseases -- Epidemiology
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Communicable diseases -- Mathematical models
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| Form |
Electronic book
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| Author |
Stechlinski, Peter, author.
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| ISBN |
9783319532080 |
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3319532081 |
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