Optimal control of an HIV infection model with logistic growth, celluar and homural immune response, cure rate and cell-to-cell spread

Abstract In this paper, we propose an optimal control problem for HIV infection model with cellular and humoral immune responses, logistic growth of uninfected cells, cell-to-cell spread, saturated infection, cure rate. The describes the interaction between infected free viruses, responses. We use two functions in our to show effectiveness drug therapy on inhibiting virus production preventing new infections. apply Pontryagin maximum principle study these functions. Next, simulate role by numerical simulations AMPL software.