
Spatial Deterministic Epidemics
American Mathematical Society (Publisher)
Will be published approx. on 28. February 2003
Book
Hardback
261 pages
978-0-8218-0499-5 (ISBN)
Description
The study of epidemic models is one of the central topics of mathematical biology. This volume is the first to present in monograph form the rigorous mathematical theory developed to analyze the asymptotic behavior of certain types of epidemic models. The main model discussed is the so-called spatial deterministic epidemic in which infected individuals are not allowed to again become susceptible, and infection is spread by means of contact distributions. Results concern the existence of traveling wave solutions, the asymptotic speed of propagation, and the spatial final size. A central result for radially symmetric contact distributions is that the speed of propagation is the minimum wave speed.Further results are obtained using a saddle point method, suggesting that this result also holds for more general situations. Methodology, used to extend the analysis from one-type to multi-type models, is likely to prove useful when analyzing other multi-type systems in mathematical biology. This methodology is applied to two other areas in the monograph, namely epidemics with return to the susceptible state and contact branching processes. This book presents an elegant theory that has been developed over the past quarter century. It will be useful to researchers and graduate students working in mathematical biology.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
College/higher education
Illustrations
bibliography, index
Weight
684 gr
ISBN-13
978-0-8218-0499-5 (9780821804995)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
(both of Queen Mary, University of London)
Content
Introduction The non-spatial epidemic Bounds on the spatial final size Wave solutions The asymptotic speed of propagation An epidemic on sites The saddle point method Epidemics with return to the susceptible state Contact branching processes Appendices Bibliography Index.