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Infectious diseases are transmitted through variousdifferent mechanisms including person to personinteractions, by insect vectors and via verticaltransmission from a parent to an unborn offspring. Thepopulation dynamics of such disease transmission can be verycomplicated and the development of rational strategies forcontrolling and preventing the spread of these diseasesrequires careful modeling and analysis.The book describes current methods for formulating modelsand analyzing the dynamics of the propagation of diseaseswhich include vertical transmission as one of the mechanismsfor their spread. Generic models that describe broad classesof diseases as well as models that are tailored to thedynamics of a specific infection are formulated andanalyzed. The effects of incubation periods, maturationdelays, and age-structure, interactions between diseasetransmission and demographic changes, population crowding,spatial spread, chaotic dynamic behavior, seasonalperiodicities and discrete time interval events are studiedwithin the context of specific disease transmission models.No previous background in disease transmission modeling andanalysis is assumedand the required biological concepts andmathematical methods are gradually introduced within thecontext of specific disease transmission models. Graphs arewidely used to illustrate and explain the modelingassumptions and results.REMARKS: NOTE: the authors have supplied variants on thepromotion text that are more suitable for promotionindifferent fields (by virtue of different emphasis in thecontent). They are not enclosed, but in the mathematicseditorial.
List of contents
1 Introduction.- 1.1 What is Vertical Transmission?.- 1.2 Methodology, Terminology and Notation.- 1.3 Examples of Vertically Transmitted Diseases.- 1.4 Organization and Principal Results.- 2 Differential Equations Models.- 2.1 A Classical Model Extended.- 2.2 Some Biological and Modeling Considerations.- 2.3 Model Without Immune Class.- 2.4 Discussion of the Global Result.- 2.5 Proofs of the Results.- 2.6 No Horizontal Transmission.- 2.7 The Model with Immune Class.- 2.8 The Case of Constant Population.- 2.9 A Model with Vaccination.- 2.10 Models with Latency or Maturation Time.- 2.11 Models with Density Dependent Death Rate.- 2.12 Parameter Estimation.- 2.13 Models of Chagas' Disease.- 2.14 An SIRS Model with Proportional Mixing.- 2.15 Evolution of Viruses.- 2.16 The Mathematical Background.- 3 Difference Equations Models.- 3.1 Introduction.- 3.2 A Model for the Transmission of Keystone Virus.- 3.3 Population Size Control via Vertical Transmission.- 3.4 Vertical Transmission in Insect Populations.- 3.5 Logistic Control in the Reproduction Rate.- 3.6 Logistic Control through the Death Terms.- 3.7 Mathematical Background.- 4 Delay Differential Equations Models.- 4.1 The Role of Delays in Epidemic Models.- 4.2 A Model with Maturation Delays.- 4.3 Delays Due to Partial Immunity.- 4.4 Delay Due to an Incubation Period.- 4.5 A Model with Spatial Diffusion.- 4.6 Diseases with Long Subclinical Periods.- 4.7 Mathematical Background.- 5 Age and Internal Structure.- 5.1 Age Structure and Vertical Transmission.- 5.2 Modeling Internal Structure.- 5.3 Derivation of the Model Equations.- 5.4 Age Structure and the Catalytic Curve.- 5.5 An s ? i Model with Vertical Transmission.- 5.6 Analysis of the Intracohort Model.- 5.7 Analysis of the Intercohort s ? i ? s Model.- 5.8Numerical Simulations.- 5.9 Global Behavior of the s ? i ? s Model.- 5.10 Destabilization Due to Age Structure.- 5.11 Thresholds in Age Dependent Models.- 5.12 Spatial Structure.- 5.13 The Force of Infection Terms.- References.- Author Index.
