Optimal Strategy for HIV Model

Abstract

The human immune-deficiency virus (HIV) with its associated acquired immune-deficiency syndrome (AIDS) is one of the pandemics that have worst-afflicted the humanity in history. A deterministic mathematical model for HIV and an optimal control model for HIV transmission dynamics that can select the best strategy was developed. The basic model being studied by exploring the basic reproduction number (which is the largest eigenvalue of the next generation matrix) as an epidemic threshold. The local and global stability of the disease-free equilibrium (DFE) shows that the disease-free equilibrium state is locally and globally asymptotically stable whenever the basic reproduction number is less than unity. Furthermore, an optimal control model for HIV incorporating three time-dependent control functions such as measures of condom use, HIV compatibility test and treatment were formulated. The corresponding optimality system was characterized and derived using Pontryagin’s maximum principle. The optimality system was numerically solved using the forward-backward Runge-Kutta method of order four. The simulated results for all possible control strategies using estimated and published parameter values showed that the model is able to select the optimal strategy. Findings from the study suggest that the combination of the three control measures can effectively reduce the spread of HIV in a community.