Wave solutions for the deterministic host-vector epidemic

Abstract

Recent papers by Atkinson and Reuter(1), Brown and Carr(5), and Barbour(2) have proved several important results concerning wave solutions of the usual deterministic model for the spatial spread of an epidemic, such as measles or influenza. In particular Atkinson and Reuter showed that non-trivial wave solutions, in a population along a line, only exist provided the contact distribution function has an exponentially bounded tail, and that the speed of propagation c must be at least some critical value c0. They constructed a solution for c > c0, which Barbour later showed to be the unique solution, modulo translation, at that speed. Brown and Carr showed that a solution was also possible at speed c0, though it has not been possible to show uniqueness at this speed.