Stability and optimal control of age-structured cell-free and cell-to-cell transmission model of HIV

The human immunodeficiency virus (HIV) can spread more efficiently when infected CD4+ T cells directly interact with uninfected T cells. This interaction forms virological synapses, which lead to the cell-to-cell transmission of HIV. This study considers an age-structured HIV infection model in which both cell-free infection and cell-to-cell transmission occur. We also incorporate the proportion of T cells in latent or exposed class. Equilibrium solutions to our model are derived and then we perform the stability analysis. Optimal control problem for the drug therapy is also considered. Forward-backward scheme is used to solve the optimal control problem numerically. Numerical simulation added to study the effect of cell-to-cell infection. The outcomes of this work are new and complement the existing ones.