Optimal Control Strategy for the Immunotherapeutic Treatment of HIV Infection with State Constraint

Abstract

This paper deals with a nonlinear model of HIV immunology which describes the interactions between the human immune system and the virus. The optimal immunotherapeutic strategies are obtained using the Pontryagin maximum principle where the state constraint is active. The aim is to find the optimal treatment strategy such that the number of uninfected CD4+T cells count at the end of treatment is maximized while minimizing the hazardous side effects of the antiretroviral drug doses as well as the systematic cost. The novelty of this work is the introduction of a state constraint in the dynamics to modify the model. The model is investigated analytically and the result is verified with numerical findings. The result of our state-constrained optimal control model shows the better effective treatment strategy for HIV infection.