On optimal controls for a general mathematical model for chemotherapy of HIV

We describe a class of optimal control problems which arise as mathematical models for biological systems in the chemotherapy of diseases which have a strong cell proliferation aspect such as cancer or AIDS. Although individually these problems are very different in their specifics, yet due to. the underlying mechanisms of cell dynamics, they also have many aspects in common and can be put into one general abstract mathematical model which encompasses them all. While on one side there is a need to consider-these problems individually to gain insight into implications for the underlying disease, on the other side there are also simplifications and insights to be gained by looking at the general properties common to all these models. In this paper we will develop and analyze such a structure in models for HIV-infection and anti-viral treatment of AIDS which have been proposed in the literature. Specifically, we give general sufficient conditions for strong local optimality of reference trajectories.