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AuthorBusenberg, Stavros. author
TitleVertically Transmitted Diseases [electronic resource] : Models and Dynamics / by Stavros Busenberg, Kenneth Cooke
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1993
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Descript XI, 248 p. online resource


Infectious diseases are transmitted through various different mechanisms including person to person interactions, by insect vectors and via vertical transmission from a parent to an unborn offspring. The population dynamics of such disease transmission can be very complicated and the development of rational strategies for controlling and preventing the spread of these diseases requires careful modeling and analysis. The book describes current methods for formulating models and analyzing the dynamics of the propagation of diseases which include vertical transmission as one of the mechanisms for their spread. Generic models that describe broad classes of diseases as well as models that are tailored to the dynamics of a specific infection are formulated and analyzed. The effects of incubation periods, maturation delays, and age-structure, interactions between disease transmission and demographic changes, population crowding, spatial spread, chaotic dynamic behavior, seasonal periodicities and discrete time interval events are studied within the context of specific disease transmission models. No previous background in disease transmission modeling and analysis is assumedand the required biological concepts and mathematical methods are gradually introduced within the context of specific disease transmission models. Graphs are widely used to illustrate and explain the modeling assumptions and results. REMARKS: NOTE: the authors have supplied variants on the promotion text that are more suitable for promotionin different fields (by virtue of different emphasis in the content). They are not enclosed, but in the mathematics editorial


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 Chagasโ{128}{153} 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 -- 5.8 Numerical 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

Mathematics Internal medicine Biomathematics Statistics Mathematics Mathematical and Computational Biology Statistics for Life Sciences Medicine Health Sciences Internal Medicine


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