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000779791 1001_ $$aLiu, Xinzhi,$$d1956-$$eauthor.
000779791 24510 $$aInfectious disease modeling :$$ba hybrid system approach /$$cXinzhi Liu, Peter Stechlinski.
000779791 264_1 $$aCham, Switzerland :$$bSpringer,$$c[2017]
000779791 300__ $$a1 online resource.
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000779791 4901_ $$aNonlinear systems and complexity,$$x2195-9994 ;$$vvolume 19
000779791 504__ $$aIncludes bibliographical references.
000779791 5050_ $$aPreface; Contents; List of Symbols; Part I Mathematical Background; 1 Basic Theory; 1.1 Preliminaries; 1.2 Ordinary Differential Equations; 1.2.1 Fundamental Theory; 1.2.2 Stability Theory; 1.2.3 Partial Stability; 1.3 Impulsive Systems; 1.4 Delay Differential Equations; 1.5 Stochastic Differential Equations; 2 Hybrid and Switched Systems; 2.1 Stability Under Arbitrary Switching; 2.2 Stability Under Constrained Switching; 2.3 Switching Control; Part II Hybrid Infectious Disease Models; 3 The Switched SIR Model; 3.1 Model Formulation; 3.2 Threshold Criteria: The Basic Reproduction Number.
000779791 5058_ $$a3.3 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.
000779791 5058_ $$a4.4.3 Waning Immunity: The Switched SIRS Model4.4.4 Passive Immunity: The Switched MSIR Model; 4.4.5 Infectious Disease Model with General Compartments; 4.4.6 Summary of Mode Basic Reproduction Numbers and Eradication Results; 4.5 Discussions; Part III Control Strategies; 5 Switching Control Strategies; 5.1 Vaccination of the Susceptible Group; 5.2 Treatment Schedules for Classes of Infected; 5.3 Introduction of the Exposed: A Controlled SEIR Model; 5.4 Screening of Traveling Individuals; 5.5 Switching Control for Vector-borne Diseases; 5.6 Discussions; 6 Pulse Control Strategies.
000779791 5058_ $$a6.1 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.
000779791 5058_ $$a7.2 Human-Mosquito Interaction Mechanisms7.3 Chikungunya Virus Model Dynamics; 7.4 Control via Mechanical Destruction of Breeding Grounds; 7.5 Control via Reduction in Contact Rate Patterns; 7.6 Control Analysis: Efficacy Ratings; 7.6.1 Assessment of Mechanical Destruction of Breeding Sites; 7.6.2 Assessment of Reduction in Contact Rate Patterns; 7.7 Discussions; Part IV Conclusions and Future Work; 8 Conclusions and Future Directions; References.
000779791 506__ $$aAccess limited to authorized users.
000779791 520__ $$aThis volume presents infectious diseases modeled mathematically, taking seasonality and changes in population behavior into account, using a switched and hybrid systems framework. The scope of coverage includes background on mathematical epidemiology, including classical formulations and results; a motivation for seasonal effects and changes in population behavior, an investigation into term-time forced epidemic models with switching parameters, and a detailed account of several different control strategies. The main goal is to study these models theoretically and to establish conditions under which eradication or persistence of the disease is guaranteed. In doing so, the long-term behavior of the models is determined through mathematical techniques from switched systems theory. Numerical simulations are also given to augment and illustrate the theoretical results and to help study the efficacy of the control schemes.
000779791 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed March 7, 2017).
000779791 650_0 $$aCommunicable diseases$$xMathematical models.
000779791 650_0 $$aCommunicable diseases$$xEpidemiology.
000779791 7001_ $$aStechlinski, Peter,$$eauthor.
000779791 77608 $$iPrint version:$$aLiu, Xinzhi, 1956-$$tInfectious disease modeling.$$dCham, Switzerland : Springer, [2017]$$z3319532065$$z9783319532066$$w(OCoLC)967549716
000779791 830_0 $$aNonlinear systems and complexity ;$$vv. 19.
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000779791 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-53208-0$$zOnline Access$$91397441.1
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