Feedback control of an HBV model based on ensemble kalman filter and differential evolution
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...
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| Format: | Article |
| Language: | English |
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AIMS Press
2018-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018030 |
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| author | Junyoung Jang Kihoon Jang Hee-Dae Kwon Jeehyun Lee |
| author_facet | Junyoung Jang Kihoon Jang Hee-Dae Kwon Jeehyun Lee |
| author_sort | Junyoung Jang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a66bd0bb5ece463c85a34c6377ae3891 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-a66bd0bb5ece463c85a34c6377ae38912025-01-24T02:40:50ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-05-0115366769110.3934/mbe.2018030Feedback control of an HBV model based on ensemble kalman filter and differential evolutionJunyoung Jang0Kihoon Jang1Hee-Dae Kwon2Jeehyun Lee3Department of Computational Science and Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul, 03722, Republic of KoreaDepartment of Mathematics, Inha University, 100 Inharo, Nam-gu, Incheon 22212, Republic of KoreaDepartment of Mathematics, Inha University, 100 Inharo, Nam-gu, Incheon 22212, Republic of KoreaDepartment of Mathematics, and Department of Computational Science and Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul, 03722, Republic of KoreaIn 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.https://www.aimspress.com/article/doi/10.3934/mbe.2018030feedback controlhbvmodel predictive controlensemble kalman filterdifferential evolution |
| spellingShingle | Junyoung Jang Kihoon Jang Hee-Dae Kwon Jeehyun Lee Feedback control of an HBV model based on ensemble kalman filter and differential evolution Mathematical Biosciences and Engineering feedback control hbv model predictive control ensemble kalman filter differential evolution |
| title | Feedback control of an HBV model based on ensemble kalman filter and differential evolution |
| title_full | Feedback control of an HBV model based on ensemble kalman filter and differential evolution |
| title_fullStr | Feedback control of an HBV model based on ensemble kalman filter and differential evolution |
| title_full_unstemmed | Feedback control of an HBV model based on ensemble kalman filter and differential evolution |
| title_short | Feedback control of an HBV model based on ensemble kalman filter and differential evolution |
| title_sort | feedback control of an hbv model based on ensemble kalman filter and differential evolution |
| topic | feedback control hbv model predictive control ensemble kalman filter differential evolution |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018030 |
| work_keys_str_mv | AT junyoungjang feedbackcontrolofanhbvmodelbasedonensemblekalmanfilteranddifferentialevolution AT kihoonjang feedbackcontrolofanhbvmodelbasedonensemblekalmanfilteranddifferentialevolution AT heedaekwon feedbackcontrolofanhbvmodelbasedonensemblekalmanfilteranddifferentialevolution AT jeehyunlee feedbackcontrolofanhbvmodelbasedonensemblekalmanfilteranddifferentialevolution |