Optimal therapy scheduling for a simplified HIV infection model

This work is motivated by the drug therapy scheduling problem in HIV infection. Using simplified switched linear system models of HIV mutation and treatment with certain class of symmetry and finite horizon cost functions, we demonstrate that the optimal state and costate trajectories lie on a sliding surface where infinitely fast switching may occur. Results suggest that in the absence of other practical constraints, switching rapidly between therapies is relevant. Simulations show the potential benefits of a proactive switching strategy to minimize viral load and delay the emergence of resistant mutant viruses.