STABILITY ANALYSIS AND OPTIMAL CONTROL FOR HIV INFECTION WITHIN-HOST MODEL WITH IMMUNE RESPONSE AND ANTIRETROVIRAL TREATMENT

Abstract

In this study, we propose a within-host treatment model for HIV infection of CD4+ T-cells. The model includes immune response, immune impairment, and antiretroviral treatment. Two types of antiretroviral drugs (reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs)) are used within the model. Positivity and boundedness of solutions are verified. We present two equilibrium points  which are infection-free and infected one. The basic reproduction number is calculated, and it becomes the threshold indicating the stability of each equilibrium point. When it is less than a unity, an infection-free equilibrium point is locally stable, whereas when it is greater than one an infected equilibrium point exists, and it is locally stable with some required conditions. Global stability of infection-free equilibrium point is obtained with some conditions. Further, we extend the model by applying optimal control problem in which both antiretroviral drugs becomes control variables. This is to minimize the HIV infection of CD4+ T-cells. Our numerical results demonstrate that RTIs drug alone could slightly reduce an HIV infection whereas the PIs drug alone gives better result in reducing the infection than RTIs drug. However, a combination of both types of drugs gives the best result for eliminating an HIV infection of CD4+ T-cells.