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 socalled 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 onetype to multitype models, is likely to prove useful when analyzing other multitype 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 nonspatial 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
