Mathematical models of HIV/AIDS and drug addiction in prisons
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Mathematical models of HIV/AIDS and drug addiction in prisons Afshin Babaei1, Hossein Jafari1,2,a , Atena Liya1 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
Received: 19 December 2019 / Accepted: 13 April 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 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.
1 Introduction Biomathematics is an interdisciplinary branch of science that concerns the applications of mathematical tools to describe the structure and behavior of biological phenomena. Mathematical modeling of dynamical systems in real world leads to better understanding the behavior of living objects [1–8]. Acquired immunodeficiency syndrome (AIDS) is a human immune system disease caused by the human immunodeficiency virus (HIV). Destroying white blood cells is the main complication of this infection [9–12]. HIV can be transmitted through various mechanisms. Having unprotected sex, sharing needles, infected blood transfusions, and transmitting the virus from the mother to the infant are the main spread factors of this virus [13–16]. In recent years, many mathematical models have been proposed to investigate the distribution of disease and to describe epidemic illnesses related to AIDS [17–26]. The ways of spreading HIV are different for various countries and places. In Iran, it is officially said that there are about 27 thousand inmates in prisons infected by HIV. But, based on unofficial statistical estimates in 2011, there were in excess of 120 thousand HIV carriers in Iranian prisons. According to the statistical estimates, 80% of infections are caused by unprotected sexual activity, and 12% by the use of HIV-infected hypodermic needles in drug addiction. However, in Iran, the consensus of expert opinion presents a dramatically different picture. Those estimates show that 45.7% of cases are caused by the injection of drugs, 37.9% by unprotected sexual activity, and 3% by mother to child transmission.
a e-mail: [email protected] (corresponding author)
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Eur. Phys. J. Plus
(2020) 135:395
In Iran, as in all countries, prisons form a key component in the spread of HIV/AIDS [27,28]. In Iran 10
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