Optimal control analysis of an HIV/AIDS model with linear incidence rate

Abstract

In this paper, a nonlinear Mathematical model is proposed to study the dynamics of HIV/AIDS in a variable size population involving two groups of infectives with different behavioral patterns and an infecting AIDS group. Basic Mathematical and epidemiological implications of the model, like the basic reproduction number and its sensitivity indexes with respect to its parameters, are derived. The basic model is modified into an optimal control problem by incorporating three controls, namely; Infection control, behavioral change efforts and administration of Highly Active Antiretroviral Therapy (HAART), aimed at controlling the spread of the disease. We examine the implementation of various combinations of the controls in order to determine the most cost effective strategy that can control the spread. Using the incremental cost-effective ratio for the various control strategies showed that the strategy that involves all the efforts is the most cost effective strategy. This reveals that the fight against the disease should be multidimensional, including treatment, education and others.