An age-structured model with immune response of HIV infection: modeling and optimal control approach

초록

We investigate the optimal treatment strategies with an age-structured model of HIV infec- tion. 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. We derive the optimal therapy protocols by formulating and analyzing an optimal control problem and establish the existence of solutions to the optimal control problem. The optimal treatment strategy is obtained by solving the corresponding optimality system numerically. We demon- strate 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 di®erent viral production rates and death rates of infected T cells.