Vertically Transmitted Diseases
Models and Dynamics
Published on 4. February 1993
Book
Hardback
XI, 248 pages
978-3-540-52004-7 (ISBN)
Description
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.
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.
More details
Series
Language
English
Place of publication
Heidelberg
Germany
Publishing group
Springer Berlin
Target group
College/higher education
Professional and scholarly
Illustrations
biography
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Weight
560 gr
ISBN-13
978-3-540-52004-7 (9783540520047)
DOI
10.1007/978-3-642-75301-5
Schweitzer Classification
Other editions
Additional editions
Book
12/2011
Springer
€53.49
Shipment within 7-9 days
Content
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.