Spatial Deterministic Epidemics

Spatial Deterministic Epidemics

by Linda Rass, John Radcliffe
     
 

This monograph presents the rigorous mathematical theory developed to analyze the asymptotic behavior of certain types of epidemic models. The main model discussed in the book 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

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Overview

This monograph presents the rigorous mathematical theory developed to analyze the asymptotic behavior of certain types of epidemic models. The main model discussed in the book 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. The authors present an elegant theory, developed over the past quarter century, that has not appeared previously in monograph form. This book will be useful to researchers and graduate students working in mathematical methods in biology.

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Product Details

ISBN-13:
9780821804995
Publisher:
American Mathematical Society
Publication date:
02/04/2003
Series:
Mathematical Surveys and Monographs, #102
Pages:
261
Product dimensions:
7.20(w) x 10.20(h) x 0.70(d)

Table of Contents

Preface
Ch. 1Introduction1
Ch. 2The non-spatial epidemic9
Ch. 3Bounds on the spatial final size27
Ch. 4Wave solutions51
Ch. 5The asymptotic speed of propagation99
Ch. 6An epidemic on sites135
Ch. 7The saddle point method153
Ch. 8Epidemics with return to the susceptible state183
Ch. 9Contact branching processes207
App. AExtended Perron-Frobenius theory227
App. BNon-negative solutions of a system of equations237
Bibliography249
Index255

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