Continuum description of a contact infection spread in a SIR model.

Abstract

We consider the process of an epidemic spread in a population of individuals with low mobility within the SIR scheme. In a continuum limit such propagation mechanism is described by a non-linear reaction-diffusion equation with a diffusion coefficient being the function of the densities of susceptible. The traveling wave solution of the corresponding system of partial differential equations is obtained and analyzed. We show that the model allows for description of Kendall epidemic waves, and give the dependence of the infection wave's shape on the parameters of the system. An explicit calculation is done for realistic values of parameters obtained from field epidemiological data for a phocine distemper virus infection among harbor seals in 1988.