A diffusion model for Aids in a closed, heterosexual population: Examining rates of infection

This paper considers a model for the spread of acquired immunodeficiency syndrome (AIDS) in a closed, purely heterosexual population. Using asymptotic expansions, the paper derives 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, it examines 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 the paper defines to be the number of different sexual partners per year, it observes through traveling wave solutions, the increase of an individual’s chance of becoming infected.