A novel mathematical model of AIDS-associated Kaposi's sarcoma: Analysis and optimal control.

Kaposi's sarcoma (KS) has been the most common HHV-8 virus-induced neoplasm associated with HIV-1 infection. Although the standard KS therapy has not changed in 20 years, not all cases of KS will respond to the same therapy. The goal of current AIDS-KS treatment modalities is to reconstitute the immune system and suppress HIV-1 replication, but newer treatment modalities are on horizon. There are very few mathematical models that have included HIV-1 viral load (VL) measures, despite VL being a key determinant of treatment outcome. Here we introduce a mathematical model that consolidates the effect of both HIV-1 and HHV-8 VL on KS tumor progression by incorporating low or high VLs into the proliferation terms of the immune cell populations. Regulation of HIV-1/HHV-8 VL and viral reservoir cells is crucial for restoring a patient to an asymptomatic stage. Therefore, an optimal control strategy given by a combined antiretroviral therapy (cART) is derived. The results indicate that the drug treatment strategies are capable of removing the viral reservoirs faster and consequently, the HIV-1 and KS tumor burden is reduced. The predictions of the mathematical model have the potential to offer more effective therapeutic interventions based on viral and virus-infected cell load and support new studies addressing the superiority of VL over CD4 T-cell count in HIV-1 pathogenesis.