HIV (human immunodeficiency virus) infection is fatal because it directly damages human's immune system by infecting CD4+ T cells. Treatment for HIV infection is a complex process that involves interactions among the virus population, the immune system and antiretroviral drugs. However, it is difficult to treat HIV infection because the high mutation rate helps HIV to escape from drug attacks. Therefore, the purpose of this paper is to seek optimal drug dosage strategy that can decrease the side effects of drugs and at the same time control HIV replication from explosion. In this paper, we use Game Theory to describe the interaction among HIV, immune system and drug. Nash Equilibrium is sought to get an equilibrium where both HIV and immune system-drug coalition can benefit most. And due to the high mutation rate of HIV, the population structure keeps changing all the time. Evolutionary Game is used among the different quasispecies of HIV population. Therefore, we use a hybrid game theory, i.e. to combine evolutionary game played by different quasispecies of HIV with conventional game played by immune system-drug coalition and the HIV population as a whole. The dosage of drug is calculated when both Evolutionary Stable Strategy (ESS) and Nash Equilibrium (NE) is satisfied. At this dosage, the drug can keep the HIV from explosively mutating into dangerous drug resistant ones while the population of CD4+ T cells remains at a proper level. This brings a new drug therapy during HIV infection to prolong the life of patient.
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