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...