Advances in Difference Equations 
Volume 2004 (2004), Issue 3, Pages 183-193
doi:10.1155/S168718390431006X

Modelling AIDS epidemic and treatment with difference equations

K. M. Tamizhmani,1 A. Ramani,2 B. Grammaticos,3 and A. S. Carstea4

 1Department of Mathematics, Pondicherry University, Kalapet, Pondicherry 605014, India
2Centre de Physique Théorique, École Polytechnique, Centre National de la Recherche Scientifique (CNRS), UMR 7644, Palaiseau 91128, France
3GMPIB, Université Paris VII, case 7021, Paris 75251, France
4Institute of Physics and Nuclear Engineering, Magurele, P.O. Box MG-6, Bucharest 76900, Romania
Received 15 October 2003; Revised 10 March 2004

Abstract

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.