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Numerical Analysis and Applications

2022 year, number 2

Behavior change a virus-resistant HIV-1 mathematical model

Rabiu Musa, Robert Willie, Nabendra Parumasur
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
Keywords: South Africa, HIV-1, resistance, behavior change, partial and total abstinence, demography


Resistance to HIV-1 disease developed by some exposed individuals has shown a promising sign in the fight against HIV-1 infection. Behavior change has also become one of the most important protection strategies against HIV-1 pandemic, but both of them have been widely neglected by mathematical modelers. In this paper, a new virus resistance HIV-1 mathematical model incorporating behavior change is formulated and analyzed rigorously for both partial and total abstinence cases. The calculated reproduction number is used to establish the local stability of the disease-free equilibrium points using the approach of Watmough and Driessche in both cases. Using appropriate demographic and epidemiological data for South Africa in the numerical simulation, the positive effect of behavior change in the midst of HIV-1 resistance is thoroughly examined, and this strategy is absolutely effective in dealing with the threat of HIV-1. This work also provides a better result than what is obtainable in the majority of the referenced related works.