STABILITY ANALYSIS AND OPTIMAL CONTROL OF AN INTRACELLULAR HIV INFECTION MODEL WITH ANTIRETROVIRAL TREATMENT

In this paper, a deterministic model describing the dynamics of the in-host HIV infection of CD4(+) T-cells is proposed. The model incorporates the presence of the CD8(+) T-cells and two types of antiretroviral drugs, for disrupting new infection and for inhibiting virus production, respectively. First, the existence, boundedness and positivity of the model solutions are shown, the basic reproduction number R-0 being then derived and shown to be a threshold value as far as the stability of the equilibria is concerned. When R-0 < 1, the infection-free equilibrium point is globally stable, whereas when R-0 > 1, the system is uniformly persistent and the infected equilibrium point is globally asymptotically stable. Further, we develop an optimal control model by taking the effect of the antiretroviral drugs to be control variables in order to minimize the HIV infection in different scenarios. By using Pontryagin's Minimum Principle and solving the model numerically, the results show that each antiretroviral drug in isolation can play a key role in reducing the count of both infected CD4(+) T-cells and HIV viruses. However, a combination of both drugs could reduce the in-host HIV infection more significantly.