Produktbild: Vertically Transmitted Diseases
Band 23

Vertically Transmitted Diseases Models and Dynamics

Aus der Reihe Biomathematics

51,99 €

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

27.12.2011

Verlag

Springer Berlin

Seitenzahl

248

Maße (L/B/H)

23,5/15,5/1,5 cm

Gewicht

405 g

Auflage

Softcover reprint of the original 1st ed. 1993

Sprache

Englisch

ISBN

978-3-642-75303-9

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

27.12.2011

Verlag

Springer Berlin

Seitenzahl

248

Maße (L/B/H)

23,5/15,5/1,5 cm

Gewicht

405 g

Auflage

Softcover reprint of the original 1st ed. 1993

Sprache

Englisch

ISBN

978-3-642-75303-9

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: GPSR Kontakt

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  • Produktbild: Vertically Transmitted Diseases
  • 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.