A Diffusion Model for AIDS in a Closed, Heterosexual Population: Examining Rates of Infection

Abstract

This paper considers a model for the spread of acquired immunodeficiency syndrome (AIDS) in a closed, purely heterosexual population. Using asymptotic expansions, we derive a set of governing partial differential equations to approximate the population of proportion infected. By assuming a very narrow distribution of partners and a closed population, we examine both the initial spread of the AIDS epidemic and specific subculture populations which lend themselves well to this scenario. A main issue explored in this paper is determining a way to estimate an individual's infection rate—the probability of becoming infected with HIV given a fixed individual risk. In particular, as an individual’s risk increases, which we define to be the number of different sexual partners per year, we observe, through traveling wave solutions, the increase of an individual’s chance of becoming infected.