Optimal treatment in a multi-strain within-host model of HIV with age structure

A multi-strain within-host model of HIV with age structure, which explicitly incorporates the loss of free viral particles due to absorption into target cells upon infection, and shedding into the environment is formulated and analyzed. In our model, a time delay between viral entry into a target cell and viral replication is incorporated, and multiple virus strains compete for a population of target cells. Control is incorporated into the model via strain-specific reverse transcriptase and protease inhibitors. An optimal control problem subject to multiple drug treatments is formulated and analyzed. Existence, characterization and uniqueness of optimal control is established. Using the forward-backward sweep numerical method, numerical simulations are presented. Simulations suggest that a combination of reverse transcriptase and protease inhibitors for each strain of the infected cells and free viruses results in a delay in initial peak in the populations of infected cells and free viruses, the absence of relapse phase within the entire time horizon of control, and a decrease in the number of infected cells and free viruses.