OPTIMAL CONTROL STRATEGY OF HIV/AIDS MODEL WITH PRE-EXPOSED PROPHYLAXIS AND BEHAVIORAL CHANG.

OPTIMAL CONTROL STRATEGY OF HIV/AIDS MODE.

Abstract

 HIV/AIDS has had a devastating global impact, particularly in underdeveloped nations where it has led to decreased life expectancy, higher mortality rates, and widespread socio-economic challenges. In contrast, developed countries have made significant progress in containing the spread and improving quality of life for those infected through advanced medical care and public health initiatives. This disparity underscores the need for effective control strategies. This study presents a six-compartment optimal control HIV/AIDS model with a constant inflow of infected immigrants. The model incorporates optimal control strategies such as public sensitization $u_1$, the Pre-Exposure Prophylaxis strategy $u_2$, screening of new arrivals $u_3$, and sexual behavioral therapy $u_4$ to minimize the spread of the disease. Pontryagin's maximum principle was employed to characterize the optimal control problem and the numerical simulation was carried out using Maple 18 software. Optimal control analysis showed that a combination of the four controls $u_1$, $u_2$, $u_3$, and $u_4$ decreased infection in all classes. The inclusion of Pre-Exposure Prophylaxis reduced the spread of HIV infection. The proposed control strategies were effective in scaling down the number of new infections despite the inflow of infective immigrants.