Strategies of optimal control for HIV spreads prevention with health campaign

Abstract

In the present paper, we discuss an HIV (Human Immunodeficiency Virus) transmission model with health information campaign about HIV control policies. The reason behind the conception of this model is the idea to divide the human population that gains awareness of HIV, due to this campaign. We assume that HIV will not infect people who are aware about the dangers of HIV. We analyze the existence and local stability of the equilibrium points. We found that the disease-free equilibrium point will be locally asymptotically stable (LAS) if the basic reproduction number (R0) is less than one, and unstable otherwise. A forward bifurcation of the system is shown numerically, depending on the intervention parameters. Some numerical simulations for the autonomous system are given to see the evolution of the system, with respect to some scenarios that might appear in the field. To accommodate the limitation of budget issue for implementation in the field, the model is reconstructed as an optimal control problem with two control variables. Numerical simulations for optimal control problems are presented for five different scenarios. Numerical simulation results suggest that controlling strategies by providing health campaigns is better, if they precede an endemic prevention strategy than endemic reduction, since the cost needed for endemic reduction is five times higher, compared with the endemic prevention. Optimal intervention should also note the value of R0. Larger control levels are needed when R0 > 1 if compared with when R0 < 1. The results of numerical simulation also show that the lower the cost of the health campaign, the more health campaigns can be provided. Based on the numerical simulation calculations, the optimal intervention of health campaign can raise public awareness about HIV, in order to reduce the number of HIV-infected individuals.