Global Stability and Optimal Control of an HIV/AIDS Epidemic Model with Behavioral Change and Treatment

In this paper, we consider a deterministic HIV/AIDS model to study the effect of information campaigns and treatment on the spread of HIV/AIDS. We demonstrate that the disease-free equilibrium is globally asymptotically stable when the basic reproduction numbers are less than one. However, if the basic reproduction number is greater than one, then a unique endemic equilibrium exists and it is globally asymptotically stable for a special case. The sensitivity analysis reveals that the effective contact rates of susceptible individuals with asymptomatic infected (pre-AIDS) individuals among other parameters contributed most significantly to the transmission and spread of HIV/AIDS. For the time-dependent controls, we formulated an appropriate optimal control problem. The Pontryagin's Maximum Principle was applied to find the necessary conditions for the existence of optimal control. The optimal system was solved using the fourth-order Runge-Kutta forward-backwards sweep method. The numerical results showed that the control strategies have a significant effect in reducing the numbers of infected individuals. The cost-effectiveness analysis reveals that the control measure implementing treatment is the most cost-effective among the strategies considered.