Dynamical models of HIV-AIDS e¤ect on population growth

We review some known dynamical models of epidemics, given by cou-pled systems of di¤erential equations, and propose a simple SI-type model of HIV-transmision that accounts for population growth. It allows exact analysis of solution and makes speci\u85c predictions on the spread of HIV and its e¤ect on populations. Then we outline an extended version of the model based on several behavioral/gender groups. We develop numerical code for solving thi system. The extended model corroborates some qual-itative predictions of simple 2D system. We compare our predictions with some recent demographic data on the spread of HIV in several African countries. The spread of epidemics could be modeled by coupled systems of di¤erential equations, representing various populations and their interactions (behavioral patterns). Such modeling aims to analyze and predict the spread of epidemics, and also develop control/prevention strategies. 1 SI and SIR models with constant population. The standard models of epidemics involve interacting populations: S- suscep