Sub-optimal switching with dwell time constraints for control of viral mutation

Regulation of mutant viri is important in many disease including HIV infection. Under current multi-drug Anti-Retroviral Therapies for HIV treatment, resistant mutations and failure to regulate viral load is typically observed after approximately 6 years. When this occurs, the current therapy must be abandoned and a new therapy initiated. An alternate approach is to treat this as a switching control problem, wherein therapy may be alternated well before virological failure is observed. In this paper we extend previous work on suboptimal control of a simplified model of HIV infection with mutations. The particular extension here is to include a `dwell time' constraint on the switching actions, that is, impose a strict minimum time between altering therapy.