Computational Modelling and Optimal Control of HIV/AIDS Transmission in a Community with Substance Abuse Problem

Abuse of substances continues to be ubiquitous in communities leading to high-risk sexual behaviour mainly due to impaired decision-making capacity. The abuse may also have numerous effects on neurocognitive function resulting in HIV infection and ultimately AIDS. In this paper, a compartmental deterministic model for the transmission dynamics of HIV/AIDS in a community plagued with substance abuse is proposed. The nonlinear problem is tackled using stability theory of differential equations and a basic reproduction number for the elimination of HIV infection is determined. The implementation of optimal control strategies involving treatment of substance-abusing susceptibles, counselling and prevention to combat the spread of HIV infection is determined using Pontryagin’s maximum principle. Numerical simulations are performed and the pertinent results are presented graphically and discussed quantitatively.

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