Eur. Phys. J. Plus (2020) 135: 395
https://doi.org/10.1140/epjp/s13360-020-00400-0

Regular Article

Mathematical models of HIV/AIDS and drug addiction in prisons

¹ Department of Mathematics, University of Mazandaran, P. O. Box 47416-95447, Babolsar, Iran
² Department of Mathematical Sciences, University of South Africa, UNISA 0003, Pretoria, South Africa

^* e-mail: jafari.usern@gmail.com

Received: 19 December 2019
Accepted: 13 April 2020
Published online: 3 May 2020

Abstract

In this study, we examine the interaction between drug addiction and the contagion of HIV/AIDS in Iranian prisons. We provide a simple mathematical model for such an interaction. The stability of drug addiction and HIV/AIDS models are analyzed separately with no medical treatment. Then, we present an improved model describing the effect of treatment of drug users on the spread of HIV/AIDS. This fully extended model is obtained by adding some new parameters for the treatment of drug addiction. The impact of rehabilitating treatments on the control of HIV/AIDS spread in prisons is investigated, and finally, the reproduction numbers are compared in cases where there is no cure or some treatment methods are available.