Spatial Deterministic Epidemics

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Brand new. We distribute directly for the publisher. 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. Read more Show Less

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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: 2/4/2003
  • 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. 1 Introduction 1
Ch. 2 The non-spatial epidemic 9
Ch. 3 Bounds on the spatial final size 27
Ch. 4 Wave solutions 51
Ch. 5 The asymptotic speed of propagation 99
Ch. 6 An epidemic on sites 135
Ch. 7 The saddle point method 153
Ch. 8 Epidemics with return to the susceptible state 183
Ch. 9 Contact branching processes 207
App. A Extended Perron-Frobenius theory 227
App. B Non-negative solutions of a system of equations 237
Bibliography 249
Index 255
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