Optimal control in HIV chemotherapy with termination viral load and latent reservoir

Damilola Olabode; Libin Rong; Xueying Wang; Damilola Olabode; Libin Rong; Xueying Wang

doi:10.3934/mbe.2019030

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 2: 619-635. doi: 10.3934/mbe.2019030

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Research article

Optimal control in HIV chemotherapy with termination viral load and latent reservoir

1.
Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164, USA
2.
Department of Mathematics, University of Florida, Gainesville, FL 32611, USA

Received: 06 February 2018 Accepted: 12 October 2018 Published: 14 January 2019

Although a number of cost-e ective strategies have been proposed for the chemotherapy of HIV infection, the termination level of viral load and latent reservoir is barely considered. However, the viral load at the termination time is an important biomarker because suppressing viral load to below the detection limit is a major objective of current antiretroviral therapy. The pool size of latently infected cells at the termination time may also play a critical role in predicting a rapid viral rebound to the pretreatment level or post-treatment control. In this work, we formulate an optimal control problem by incorporating the termination level in terms of viral load, latently and productively infected T cells into an existing HIV model. The necessary condition for this optimal system is derived using the Pontryagin's maximum principle. Numerical analysis is carried out using Runge-Kutta 4 method for the forward-backward sweep. Our results suggest that introducing the termination viral load into the control provides a better strategy in HIV chemotherapy.
- HIV-1,
- latency,
- chemotherapy,
- ART/HAART,
- termination level,
- optimal control
Citation: Damilola Olabode, Libin Rong, Xueying Wang. Optimal control in HIV chemotherapy with termination viral load and latent reservoir[J]. Mathematical Biosciences and Engineering, 2019, 16(2): 619-635. doi: 10.3934/mbe.2019030

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Abstract

Although a number of cost-e ective strategies have been proposed for the chemotherapy of HIV infection, the termination level of viral load and latent reservoir is barely considered. However, the viral load at the termination time is an important biomarker because suppressing viral load to below the detection limit is a major objective of current antiretroviral therapy. The pool size of latently infected cells at the termination time may also play a critical role in predicting a rapid viral rebound to the pretreatment level or post-treatment control. In this work, we formulate an optimal control problem by incorporating the termination level in terms of viral load, latently and productively infected T cells into an existing HIV model. The necessary condition for this optimal system is derived using the Pontryagin's maximum principle. Numerical analysis is carried out using Runge-Kutta 4 method for the forward-backward sweep. Our results suggest that introducing the termination viral load into the control provides a better strategy in HIV chemotherapy.

References

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