A Game Theoretical Approach to Optimal Control of Dual Drug Delivery for HIV Infection Treatment

For human immunodeficiency virus (HIV) infection treatment, the host immune system and antiviral drugs form a coalition to fight against HIV. Evidence suggests that drug therapy with Highly Active Antiretroviral Therapy can effectively prolong the life of the patient because it can reduce the replication of HIV while, at the same time, protecting the CD4+ T cells. The dosages of different drugs, however, are important in determining the success of the treatment. In addition, drug therapy for HIV is complicated by the fact that viruses can mutate, thereby effectively escaping from the attack of the drugs. This paper models HIV drug therapy by considering a game between HIV and a coalition consisting of both antiviral drugs and the host immune system. The Nash equilibrium (NE) is calculated as the solution of the game. The simulation results show that an NE exists in which both T cells and viruses remain and coexist after several generations. This brings a new drug therapy during HIV infection to prolong the life of the patient with HIV coexistence.