Modelling AIDS epidemic and treatment with difference equations

We propose two models for the description of the dynamics of an AIDS epidemic and of the effect of a combined-drugs AIDS treatment based on difference equations. We show that our interacting population model, despite its extreme simplicity, describes adequately the evolution of an AIDS epidemic. Acellular-automaton analogue of the discrete system of equationsis presented as well. In the case of drug treatment, we identify two different regimes corresponding to efficient and inefficient medication. The effect of the discreteness of the equations is also studied.