Báo Cáo Báo cáo hóa học MODELLING AIDS EPIDEMIC AND TREATMENT WITH DIFFERENCE EQUATIONS

MODELLING AIDS EPIDEMIC AND TREATMENT WITH DIFFERENCE EQUATIONS K. M. TAMIZHMANI, A. RAMANI, B. GRAMMATICOS, AND A. S. CARSTEA Received 15 October 2003 and in revised form 10 March 2004

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. A cellular-automaton analogue of the discrete system of equations is 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.

1. Introduction The modelling of biological systems goes back in time to an era when the very word “modelling,” in the present acceptation, was unknown. The use of mathematical modelling, which has met with such a great success in