The study of epidemic models is one of the central topics of
mathematical biology. This volume presents in monograph form the
rigorous mathematical theory developed to analyze the asymptotic
behaviour 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 travelling 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.
