Optimal control for HIV treatment

Gordon Akudibillah; Abhishek Pandey; Jan Medlock; Gordon Akudibillah; Abhishek Pandey; Jan Medlock

doi:10.3934/mbe.2019018

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 1: 373-396. doi: 10.3934/mbe.2019018

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Research article

Optimal control for HIV treatment

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

Received: 23 January 2018 Accepted: 01 September 2018 Published: 14 December 2018

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.
- HIV/AIDS,
- HIV clinical stages,
- mathematical model,
- treatment,
- optimal control
Citation: Gordon Akudibillah, Abhishek Pandey, Jan Medlock. Optimal control for HIV treatment[J]. Mathematical Biosciences and Engineering, 2019, 16(1): 373-396. doi: 10.3934/mbe.2019018

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Abstract

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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