Optimal control and sensitivity analysis of HIV model with public health education campaign and antiretroviral therapy

Abstract

A deterministic mathematical model with public health education campaigns and antiretroviral therapy as control variables are formulated and analyzed using sensitivity analysis and optimal control theory (Pontryagin’s Maximum Principle). The sensitivity analysis shows that by increasing the public health education campaign for susceptible individuals and providing antiretroviral therapy to infected individuals in the symptomatic stage has an effect in reducing the spread of the HIV infection. The most sensitive parameter is the efficacy rate of the public health education campaign, followed by the contact rate of susceptibles with an infective in the asymptomatic stage, followed by the progression rate from the infected class into the pre-AIDS class. The least sensitive parameter is the natural death rate. The numerical simulation of both systems, i.e. with control and without control shows that the combination of the two strategies helps to make a significant reduction in the number of infectives in the asymptomatic stage, the number of individuals in the pre-AIDS stage, and the number of individuals with full-blown AIDS.