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E-raamat: Infectious Disease Modeling: A Hybrid System Approach

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Infectious Disease Modeling: A Hybrid System ApproachSuurem pilt
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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.


Arvustused

If you have a serious interest in the epidemiology of infectious diseases and are eager to roll up your sleeves, please consult this book . (Odo Diekmann, SIAM Review, Vol. 61 (1), March, 2019)

This book focuses on infectious disease mathematical models, taking seasonality and changes in population behavior into account, using a switched and hybrid systems framework. This book is strongly recommended to graduate level students with a background in dynamic system or epidemic modeling and an interest in mathematical biology, epidemic models, and physical problems exhibiting a mixture of continuous and discrete dynamics. (Hemang B. Panchal, Doodys Book Reviews, April, 2017)

This book presents a new type of switched model for the spread of infectious diseases. This book should be useful and attractive for students and researchers seeking updated progresses in the fieldof epidemic modeling . (Yilun Shang, zbMATH 1362.92002, 2017)

Part I Mathematical Background
1 Basic Theory
3(18)
1.1 Preliminaries
3(2)
1.2 Ordinary Differential Equations
5(9)
1.2.1 Fundamental Theory
5(2)
1.2.2 Stability Theory
7(6)
1.2.3 Partial Stability
13(1)
1.3 Impulsive Systems
14(2)
1.4 Delay Differential Equations
16(2)
1.5 Stochastic Differential Equations
18(3)
2 Hybrid and Switched Systems
21(22)
2.1 Stability Under Arbitrary Switching
25(2)
2.2 Stability Under Constrained Switching
27(3)
2.3 Switching Control
30(13)
Part II Hybrid Infectious Disease Models
3 The Switched SIR Model
43(40)
3.1 Model Formulation
43(6)
3.2 Threshold Criteria: The Basic Reproduction Number
49(3)
3.3 Seasonal Variations in Disease Transmission: Term-Time Forcing
52(3)
3.4 Adding Population Dynamics: The Classical Endemic Model
55(14)
3.5 Generalizing the Incidence Rate of New Infections
69(5)
3.6 Uncertainty in the Model: Stochastic Transmission
74(7)
3.7 Discussions
81(2)
4 Epidemic Models with Switching
83(52)
4.1 Absence of Conferred Natural Immunity: The SIS Model
83(14)
4.2 Multi-City Epidemics: Modeling Traveling Infections
97(11)
4.3 Vector-Borne Diseases with Seasonality
108(4)
4.4 Other Epidemiological Considerations
112(17)
4.4.1 Vertical Transmission
112(3)
4.4.2 Disease-Induced Mortality: Varying Population Size
115(5)
4.4.3 Waning Immunity: The Switched SIRS Model
120(2)
4.4.4 Passive Immunity: The Switched MSIR Model
122(2)
4.4.5 Infectious Disease Model with General Compartments
124(3)
4.4.6 Summary of Mode Basic Reproduction Numbers and Eradication Results
127(2)
4.5 Discussions
129(6)
Part III Control Strategies
5 Switching Control Strategies
135(44)
5.1 Vaccination of the Susceptible Group
135(11)
5.2 Treatment Schedules for Classes of Infected
146(5)
5.3 Introduction of the Exposed: A Controlled SEIR Model
151(9)
5.4 Screening of Traveling Individuals
160(5)
5.5 Switching Control for Vector-borne Diseases
165(11)
5.6 Discussions
176(3)
6 Pulse Control Strategies
179(48)
6.1 Public Immunization Campaigns: Control by Pulse Vaccination and Treatment
179(38)
6.1.1 Impulsive Control Applied to the Classical Endemic Model
180(6)
6.1.2 Incorporating Impulsive Treatment into the Public Campaigns
186(4)
6.1.3 The SIR Model with General Switched Incidence Rates
190(4)
6.1.4 Vaccine Failures
194(3)
6.1.5 Pulse Control Applied to an Epidemic Model with Media Coverage
197(7)
6.1.6 Multi-City Vaccination Efforts
204(6)
6.1.7 Pulse Vaccination Strategies for a Vector-Borne Disease
210(7)
6.2 Discussions
217(10)
6.2.1 Comparison of Control Schemes
219(8)
7 A Case Study: Chikungunya Outbreak in Reunion
227(34)
7.1 Background
227(3)
7.2 Human--Mosquito Interaction Mechanisms
230(3)
7.3 Chikungunya Virus Model Dynamics
233(2)
7.4 Control via Mechanical Destruction of Breeding Grounds
235(11)
7.5 Control via Reduction in Contact Rate Patterns
246(2)
7.6 Control Analysis: Efficacy Ratings
248(8)
7.6.1 Assessment of Mechanical Destruction of Breeding Sites
250(4)
7.6.2 Assessment of Reduction in Contact Rate Patterns
254(2)
7.7 Discussions
256(5)
Part IV Conclusions and Future Work
8 Conclusions and Future Directions
261(4)
References 265
Xinzhi Liu is a Professor of Mathematics at the University of Waterloo. Peter Stechlinski is a Postdoctoral Fellow in the Process Systems Engineering Laboratory at the Massachusetts Institute of Technology
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