Feedback control of an HBV model based on ensemble kalman filter and differential evolution

Junyoung Jang; Kihoon Jang; Hee-Dae Kwon; Jeehyun Lee; Junyoung Jang; Kihoon Jang; Hee-Dae Kwon; Jeehyun Lee

doi:10.3934/mbe.2018030

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 3: 667-691. doi: 10.3934/mbe.2018030

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Feedback control of an HBV model based on ensemble kalman filter and differential evolution

1.
Department of Computational Science and Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul, 03722, Republic of Korea
2.
Department of Mathematics, Inha University, 100 Inharo, Nam-gu, Incheon 22212, Republic of Korea
3.
Department of Mathematics, and Department of Computational Science and Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul, 03722, Republic of Korea

Received: 13 March 2017 Revised: 14 September 2017 Published: 01 June 2018
MSC : Primary: 92B05; Secondary: 49K15

In this paper, we derive efficient drug treatment strategies for hepatitis B virus (HBV) infection by formulating a feedback control problem. We introduce and analyze a dynamic mathematical model that describes the HBV infection during antiviral therapy. We determine the reproduction number and then conduct a qualitative analysis of the model using the number. A control problem is considered to minimize the viral load with consideration for the treatment costs. In order to reflect the status of patients at both the initial time and the follow-up visits, we consider the feedback control problem based on the ensemble Kalman filter (EnKF) and differential evolution (DE). EnKF is employed to estimate full information of the state from incomplete observation data. We derive a piecewise constant drug schedule by applying DE algorithm. Numerical simulations are performed using various weights in the objective functional to suggest optimal treatment strategies in different situations.
- Feedback control,
- HBV,
- model predictive control,
- ensemble Kalman filter,
- differential evolution
Citation: Junyoung Jang, Kihoon Jang, Hee-Dae Kwon, Jeehyun Lee. Feedback control of an HBV model based on ensemble kalman filter and differential evolution[J]. Mathematical Biosciences and Engineering, 2018, 15(3): 667-691. doi: 10.3934/mbe.2018030

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Abstract

In this paper, we derive efficient drug treatment strategies for hepatitis B virus (HBV) infection by formulating a feedback control problem. We introduce and analyze a dynamic mathematical model that describes the HBV infection during antiviral therapy. We determine the reproduction number and then conduct a qualitative analysis of the model using the number. A control problem is considered to minimize the viral load with consideration for the treatment costs. In order to reflect the status of patients at both the initial time and the follow-up visits, we consider the feedback control problem based on the ensemble Kalman filter (EnKF) and differential evolution (DE). EnKF is employed to estimate full information of the state from incomplete observation data. We derive a piecewise constant drug schedule by applying DE algorithm. Numerical simulations are performed using various weights in the objective functional to suggest optimal treatment strategies in different situations.

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