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Spatial Deterministic Epidemics
Linda Rass and John Radcliffe, Queen Mary, University of London, England
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Mathematical Surveys and Monographs
2003; 261 pp; hardcover
Volume: 102
ISBN-10: 0-8218-0499-5
ISBN-13: 978-0-8218-0499-5
List Price: US$76
Member Price: US$60.80
Order Code: SURV/102
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Mathematical Biology - Mark A Lewis, Mark A J Chaplain, James P Keener and Philip K Maini

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.

Readership

Graduate students and research mathematicians interested in mathematical biology.

Reviews

"The material of the book is presented in full detail ... a thorough account ... with a nice and rather complete bibliography ... a useful reference source for forthcoming research in the field."

-- Mathematical Reviews

Table of Contents

  • 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
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