Significant Parameters in the HIV/AIDS Transmission and Control Optimal Problem

Abstract

This article studies how to figure out important parameters in the HIV/AIDS model using sensitivity analysis. The parameters that arise in the basic-reproduction number (R0) are calculated to get the sensitivity index. We get two significant parameters, Ω and β2, the recruitment rate of uneducated subpopulation and transmission rate from uneducated individual to infected individual taking ARV, respectively. These parameters give a higher contribution to the transmission of HIV. Furthermore, we conduct the problem of optimal control on the mathematical model of the spread of HIV/AIDS to minimize HIV-infected individuals. We propose two controls, public education and ARV treatment. We establish the existence of an optimal control pair. The Pontryagin minimum principle is used to obtain the best conditions to control the disease transmission. Numerical simulations were conducted to get the results of the analysis. The results show that a combination of public education and ARV treatment helps to control the spread of HIV disease and to get the minimum cost related to the realization of controls.

Key words and phrases. Sensitivity analysis, Optimal control, HIV/AIDS model, the Pontryagins minimum principle.

2010 Mathematics Subject Classification. 49J15, 49K15, 26D10