Vertically transmitted diseases. Models and dynamics.

*(English)*Zbl 0837.92021
Biomathematics (Berlin). 23. Berlin: Springer-Verlag. xi, 248 p. (1993).

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 and newborn offspring. This 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 behavior, seasonal periodicities and discrete time interval events are studied within the context of specific disease transmission models.

The mathematical prerequisites for reading most of the book consist of a working knowledge of calculus and an acquaintance with differential equations and linear algebra. No previous background in disease transmission modeling and analysis is assumed and the required biological concepts and mathematical methods are gradually introduced within the context of specific disease transmission models. The book is addressed to modelers, biologists and epidemiologists who are interested in general principles, and to applied mathematicians.

The mathematical prerequisites for reading most of the book consist of a working knowledge of calculus and an acquaintance with differential equations and linear algebra. No previous background in disease transmission modeling and analysis is assumed and the required biological concepts and mathematical methods are gradually introduced within the context of specific disease transmission models. The book is addressed to modelers, biologists and epidemiologists who are interested in general principles, and to applied mathematicians.

Reviewer: G.Hasibeder (Wien)

##### MSC:

92D30 | Epidemiology |

92-02 | Research exposition (monographs, survey articles) pertaining to biology |

92-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology |