Analysis and Control of an HIV Infection Model With Cell‐to‐Cell Transmission and Saturated Incidence Rate

Research shows that the saturated incidence rate is closer to the process of infection than the bilinear incidence rate. In this paper, we propose an HIV model with cell‐to‐cell transmission and saturated incidence rate, in which both cell‐mediated and humoral immune responses are considered. We analyze the model by showing the positivity and boundedness of the solution, calculating the steady states, and proving the local stability of the steady states. Then we formulate the optimal control problem to find the optimal treatment strategies that minimize the concentration of infected CD4+ T cells as well as free virus, keeping the side effects of antiretroviral drugs as low as possible in a fixed time. We establish and analyze the objective functions of linear control and quadratic control. Numerical simulations are carried out to verify the corresponding theoretical results and show the optimal control strategies and their effects on cell concentrations.