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Abstract
Optimal control theory is applied to a mathematical model that describes the interaction of the immune system with the human immunodeficiency virus (HIV) and that permits the administration of triple HIV drug therapy. The optimal control represents a percentage effect the chemotherapy consisting of fusion inhibitors (FIs), reverse transcriptase inhibitors (RTIs), and protease inhibitors (PIs) has on the interaction of CD4+T-cells with the virus. First, we maximize the benefit based on the T-cell count and minimize the systemic cost based on the percentage of chemotherapies given and then build an objective functional to minimize the viral replication and treatment systemic costs. Our results indicate that highly toxic drugs and small dosage sizes have the potential for improving the quality of life and reducing economic costs of therapy. An optimal control strategy that seeks to maximize CD4+ T-cells has the potential to provide better treatment results over the optimal treatmet strategy that seeks to minimize the viral production. The addition of FIs to the current HIV treatment strategy of RTIs and PIs improves to relax both concentration and dose sizes of RTIs and PIs.