Optimal controls analysis of HIV/AIDS transmission model with an aware population

Abstract

In this paper, a mathematical model that describes the transmission dynamics of HIV/AIDS with an awareness effect is studied. We analyze the existence and stability of the model equilibriums of HIV/AIDS based on the basic reproduction number. Parameter sensitivity analysis was also conducted to determine the most influential parameters on the spread of this disease. Furthermore, we apply the optimal controls on the HIV model in the form of prevention, campaign, and treatment of Antiretroviral Therapy (ART). The optimal control problems are solved using Pontryagin's Maximum Principle. Numerical simulation results show that the combination of prevention and campaign effort can effectively minimize the number of human populations infected with HIV/AIDS.