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

Junyoung Jang, Kihoon Jang, Hee Dae Kwon, Jeehyun Lee

Research output: Contribution to journalArticle

2 Citations (Scopus)

### 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.

Original language English 667-691 25 Mathematical Biosciences and Engineering 15 3 https://doi.org/10.3934/mbe.2018030 Published - 2018 Jun

### Fingerprint

Ensemble Kalman Filter
Hepatitis B virus
Differential Evolution
Viruses
Kalman filters
Feedback Control
Virus
Feedback control
Control Problem
Virus Diseases
Model-based
Drug therapy
Infection
Drugs
qualitative analysis
infection
dynamic models
drug therapy
Reproduction number

### All Science Journal Classification (ASJC) codes

• Modelling and Simulation
• Agricultural and Biological Sciences(all)
• Computational Mathematics
• Applied Mathematics

### Cite this

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title = "Feedback control of an HBV model based on ensemble kalman filter and differential evolution",
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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Feedback control of an HBV model based on ensemble kalman filter and differential evolution. / Jang, Junyoung; Jang, Kihoon; Kwon, Hee Dae; Lee, Jeehyun.

In: Mathematical Biosciences and Engineering, Vol. 15, No. 3, 06.2018, p. 667-691.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Feedback control of an HBV model based on ensemble kalman filter and differential evolution

AU - Jang, Junyoung

AU - Jang, Kihoon

AU - Kwon, Hee Dae

AU - Lee, Jeehyun

PY - 2018/6

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AB - 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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