Pre-exposure prophylaxis HIV/AIDS mathematical model with non classical isolation
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Pre‑exposure prophylaxis HIV/AIDS mathematical model with non classical isolation P. M. Tchepmo Djomegni1,2 · Andualem Tekle1 · Mohammed Y. Dawed3 Received: 11 November 2019 / Revised: 6 March 2020 © The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2020
Abstract We propose a mathematical model to understand the transmission dynamics of HIV/ AIDS in an environment. In addition to previous approaches, we incorporate two classes of isolated. By isolated we do not mean physical separation, but commitment to keep its status. We establish the well-posedness of our model and fully analyze the asymptotic behavior of the solutions which depends on the basic reproduction number R0 . We then perform sensitive analysis to investigate the best strategy to keep the average number of secondary infection R0 low. Our investigation reveals that when there is both high awareness and high efficacy of PrEP (pre-exposure prophylaxis) use, increasing the efficacy of PrEP use decreases R0 the most. Otherwise, the best strategy is to isolated more susceptible to the class H1 . Our model can be applied to any organizations/companies relying on physical labor forces (with some workers being infected by HIV/AIDS). Keywords Compartmental model · HIV/AIDS model · Pre-exposure prophylaxis (PrEP) Mathematics Subject Classification 34E10c · 34A02 · 34D20 · 34C60 · 92B05
1 Introduction The acquired immuno-deficiency Syndrome (AIDS) is an infection caused by the human immuno-deficiency virus (HIV). The virus infects the T-helper lymphocytes cells responsible to coordinate the actions of other immune system cells. These * P. M. Tchepmo Djomegni [email protected] 1
Department of Mathematics, Arba Minch University, PO Box 21, Arba Minch, Ethiopia
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School of Mathematical and Statistical Sciences, North West University, Private Bag X6001, Potchefstroom, South Africa
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School of Mathematical and Statistical Sciences, Hawassa University, Awassa, Ethiopia
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cells are targeted because there is a protein called CD4 on their surface. The virus attaches to the protein CD4, then invades the T-helper cell and produces new copies able to infect other T-helper cells. This is the reason why T-helper cell is referred to CD4+ T . When the number of the CD4+ T cells is less than 200/mm3 the infected individual is declared HIV positive. HIV can be transmitted through sexual intercourse, blood transfusion, contaminated sharp materials and mother-to-child transmission. Transmission as the result of sexual intercourse accounts for third-quarters of all HIV infections in the world-wide. This justifies the classification of HIV/AIDS as being a sexually transmitted diseases [15]. HIV undergoes four stages/phases to reach AIDS. These are: primary HIV infection stage, chronic stage, pre-AIDS stage and AIDS. AIDS was first recognized in 1981 among homosexual men in the USA [7, 17]. The virus had expanded unnoticedly and unsuspectedly in the mid-1980s throughout the world. Currently HIV
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