Author | Busenberg, Stavros. author |
---|---|
Title | Vertically Transmitted Diseases [electronic resource] : Models and Dynamics / by Stavros Busenberg, Kenneth Cooke |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1993 |
Connect to | http://dx.doi.org/10.1007/978-3-642-75301-5 |
Descript | XI, 248 p. online resource |
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 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