Numerical simulations of the spread of rabies in two-dimensional space

Abstract

We extend our previous work on the spatial spread of fox rabies from one dimension to two dimensions. We consider the case when the latent period has fixed length. We use the method of lines to replace the spatial derivatives and the integral equations with algebraic approximations, then we apply the explicit continuous Runge–Kutta method of fourth order and discrete Runge–Kutta method of third order with six stages to numerically integrate the resulting systems of ordinary and delay differential equations. We discuss and confirm some of the major results we obtained in earlier work. The asymptotic speeds of spread observed in the two-dimensional simulations and in earlier work are discussed and compared with those found in nature.