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Modelling Optimal Control of Heavy Alcohol Consumption on the Transmission Dynamics of HIV/AIDS

Emmanuel Ongodia, Gasper G. Mwanga

Abstract

communities leading to behavioural and physiological effects on neuro-cognitive function. This results into high-risk sexual behaviour mainly due to impaired decision-making capacity and impulsivity, a catalyst of HIV infection and ultimately AIDS. This paper investigates the best control combination for HIV/AIDS pandemic in a community with alcohol abuse problem. It proposes a compartmental deterministic model for the transmission dynamics of HIV/AIDS in a community plagued with alcohol abuse. The paper determines the implementation of optimal control strategies involving reduction of new HIV cases through the ABC (abstinence, being faithful, and use of condoms) campaign, treatment of alcohol abusers and prevention of alcohol relapse using Pontryagin's maximum principle. Numerical simulations are implemented using the forward-backward sweep method, and the pertinent results are presented graphically and discussed quantitatively. Based on performance, results from numerical simulations depict that the best results are obtained when the three strategies are used simultaneously.

 

Keywords

HIV/AIDS; alcohol; optimal control; ABC strategy; treatment; relapse.

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