Optimal control of an age-structured model of HIV infection

The optimal treatment strategies with an age-structured model of HIV infection are investigated. The age-structured model allows for variations in the virion production rate and the death rate of infected T cells as a function of age, which is the length of time since infection. The optimal therapy protocol is derived by formulating and analyzing an optimal control problem and the existence of solutions to the optimal control problem is established. The optimal treatment strategy is obtained by solving the corresponding optimality system numerically. It is demonstrated by numerical simulations that the dynamic treatment strategy delays the time to reach the peak viral load and reduces the viral load. Moreover, we propose that optimal therapy protocols should be changed according to different viral production rates and death rates of infected T cells.