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Vertically transmitted diseases : models and dynamics

Author: Stavros N Busenberg; Kenneth L Cooke
Publisher: Berlin ; New York : Springer-Verlag, ©1993.
Series: Biomathematics (Berlin, Germany), v. 23.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Describes methods for formulating models and analyzing the dynamics of the propagation of diseases, including vertical transmission as one of the mechanisms for their spread. The required biological  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Stavros N Busenberg; Kenneth L Cooke
ISBN: 9783540520047 354052004X 9780387520049 038752004X
OCLC Number: 28377559
Description: xi, 248 pages : illustrations.
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.- 2.7.1 The SIR Model with Vaccination.- 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.- 2.13.1 Proportional Mixing and Vector Transmission.- 2.13.2 An SIS Model with Proportional Mixing.- 2.13.3 Logistic Control.- 2.14 An SIRS Model with Proportional Mixing.- 2.15 Evolution of Viruses.- 2.16 The Mathematical Background.- 2.16.1 Positivity and Invariant Regions.- 2.16.2 Equilibria and Stability Analysis.- 2.16.3 Global Stability in One and Two Dimensions.- 2.16.4 General Global Stability.- 2.16.5 A Special Global Stability Result.- 2.16.6 Existence and Bifurcation of Periodic Solutions.- 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.- 3.3.1 Fine Structure of Population Size Control.- 3.3.2 Proofs of the Theorems.- 3.4 Vertical Transmission in Insect Populations.- 3.5 Logistic Control in the Reproduction Rate.- 3.5.1 Complicated Dynamics and Long Term Transients.- 3.6 Logistic Control through the Death Terms.- 3.6.1 Synchronous Oviposition.- 3.6.2 Distributed Asynchronous Oviposition.- 3.7 Mathematical Background.- 3.7.1 Positivity and Invariant Regions.- 3.7.2 Equilibria and Stability Analysis.- 3.7.3 Global Stability.- 3.7.4 Periodic Solutions, Bifurcation and Chaos.- 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.- 4.7.1 Positivity and Invariant Regions.- 4.7.2 Equilibria and Stability Analysis.- 4.7.3 Liapunov Stability Theory.- 4.7.4 Existence and Bifurcation of Periodic Solutions.- 4.7.5 Invariant Integral Conditions.- 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.
Series Title: Biomathematics (Berlin, Germany), v. 23.
Responsibility: Stavros Busenberg, Kenneth Cooke.
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