Mathematical Biosciences and Engineering, 2019, 16(1): 373-396. doi: 10.3934/mbe.2019018 Research article

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Optimal control for HIV treatment

Gordon Akudibillah, Abhishek Pandey, Jan Medlock

1 Department of Environmental Sciences, Oregon State University, Corvallis, Oregon 97331, USA
2 Center for Infectious Disease Modeling and Analysis, Yale University, New Haven, Connecticut 06511, USA
3 Department of Biomedical Sciences, Oregon State University, Corvallis, Oregon 97331, USA

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Apart from the traditional role of preventing progression from HIV to AIDS, antiretroviral drug therapy (ART) has been shown to have the additional benefit of substantially reducing infectiousness in infected people, making ART potentially an important strategy in the fight against HIV. We developed a mathematical model based on the WHO’s 5-stage classification of HIV/AIDS disease progression. Our model stratifies the population by disease stage, diagnosis and treatment. We used optimal control methods and data from South Africa to determine the best time-dependent treatment allocation required to minimize new infections, infection-years, deaths and cost. Our results indicated that the treatment strategy to minimize infection-years and new infections is to place emphasis on early treatment (i.e., treatment in Stage II & III), while to minimize cost and death, the emphasis should be on late treatment (i.e., Stage III & IV). Applying the optimal treatment strategy also leads to a substantial reduction in disease incidence and prevalence. The results of this study will hopefully provide some guidance for policymakers in determining how to best allocate antiretroviral drugs in order to maximize the benefits of treatment.

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