A Mathematical Model for the Spatial Spread of HIV in a Heterogeneous Population

Abstract

An important factor in the dynamic transmission of HIV is the spatio-temporal mobility of the host population. One key challenge in HIV epidemiology therefore, is determining how the spatial structure of the host population influences disease transmission. The aim of this paper is to study how the movement of individuals impacts the spatial spread of HIV. We constructed a deterministic reaction-diffusion equation model for the spread of HIV in a heterosexually mobile population, under the assumption of a varying population size to study the dynamics of HIV spread in a spatially structured population and obtained the minimal wave speed. Then we considered the existence of traveling waves and the influences of parameters on HIV prevalence and the minimal wave speed. Numerical simulation showed that a stationary labyrinthine pattern emerges in the distribution of the infection population density in the two high-risk groups as a result of diffusion.

Keywords: Spatial distribution, HIV, reaction-diffusion, epidemiology.