TRANSMISSION DYNAMICS OF HIV/AIDS WITH OPTIMAL CONTROL IN THE PRESENCE OF CAREFREE SUSCEPTIBLES AND TREATMENT

摘要

The aim of this paper is to investigate the effectiveness of HIV/AIDS preventive and treatment measures (treatment of HIV individuals, treatment of AIDS individuals, enlightenment campaign and recruitment rate of carefree susceptibles) in reducing the spread of the disease. For this, we consider a mathematical model for the transmission dynamics of the disease that includes these measures. We first consider the constant control case, we calculate the basic reproduction number and investigate the existence and stability of equilibria. The model is found to exhibit backward bifurcation implying that for the disease to be eradicated, the basic reproductive number must be below a critical value less than one. In the time dependent control case, we use Pontryagin's Maximum Principle to derive necessary conditions for the optimal control of the disease. Finally, numerical simulations are performed to illustrate the analytical results.