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

  • 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.

    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

    Related Papers:

  • 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.


    加载中
    [1] [ Z. Abbas,A. R. Siddiqui, Management of hepatitis B in developing countries, World Journal of Hepatology, 3 (2011): 292-299.
    [2] [ D. Lavanchy, Hepatitis B virus epidemiology, disease burden, treatment, and current and emerging prevention and control measures, Journal of Viral Hepatitis, 11 (2004): 97-107.
    [3] [ B. M. Adams,H. T. Banks,M. Davidian,Hee-Dae Kwon,H. T. Tran,S. N. Wynne,E. S. Rosenberg, HIV dynamics: Modeling, data analysis, and optimal treatment protocols, Journal of Computational and Applied Mathematics, 184 (2005): 10-49.
    [4] [ K. Blayneh,Y. Cao,H.-D. Kwon, Optimal control of vector-borne diseases: Treatment and prevention, Discrete and Continuous Dynamical Systems-series B, 11 (2009): 587-611.
    [5] [ F. Brauer, P. Van den Driessche and J. Wu, Mathematical Epidemiology, Springer-Verlag, Berlin, Heidelberg, 2008.
    [6] [ C. Castillo-Chavez, Blower, P. van den Driessche, D. Kirschner and A. -A. Yakubu, Mathematical Approaches for Emerging and Reemerging Infectious Diseases, Springer-Verlag, New York, 2002.
    [7] [ F. Daum, Nonlinear filters: beyond the Kalman filter, IEEE Aerospace and Electronic Systems Magazine, 20 (2005): 57-69.
    [8] [ G. Evensen, Data Assimilation: The Ensemble Kalman Filter, Springer-Verlag Berlin Heidelberg, 2009.
    [9] [ T. Fujimoto,R. R. Ranade, Two Characterizations of Inverse-Positive Matrices: The Hawkins-Simon Condition and the Le Chatelier-Braun Principle, Electronic Journal of Linear Algebra, 11 (2004): 59-65.
    [10] [ J. Guedj,Y. Rotman,S. J. Cotler,C. Koh,P. Schmid, Understanding early serum hepatitis D virus and hepatitis B surface antigen kinetics during pegylated interferon-alpha therapy via mathematical modeling, Hepatology, 60 (2014): 1902-1910.
    [11] [ L. G. Guidotti,R. Rochford,J. Chung,M. Shapiro,R. Purcell, Viral clearance without destruction of infected cells during acute HBV infection, Science, 284 (1999): 825-829.
    [12] [ K. Ito,K. Kunisch, Asymptotic properties of receding horizon optimal control problems, SIAM Journal on Control and Optimization, 40 (2002): 1585-1610.
    [13] [ H. Y. Kim, H. -D. Kwon, T. S. Jang, J. Lim and H. Lee, Mathematical modeling of triphasic viral dynamics in patients with HBeAg-positive chronic hepatitis B showing response to 24-week clevudine therapy, PloS One, 7 (2012), e50377.
    [14] [ S. B. Kim, M. Yoon, N. S. Ku, M. H. Kim and J. E. Song, et, al., Mathematical modeling of HIV prevention measures including pre-exposure prophylaxis on hiv incidence in south korea, PloS One, 9 (2014), e90080.
    [15] [ J. Lee,J. Kim,H.-D. Kwon, Optimal control of an influenza model with seasonal forcing and age-dependent transmission rates, Journal of Theoretical Biology, 317 (2013): 310-320.
    [16] [ S. Lee,M. Golinski,G. Chowell, Modeling optimal age-specific vaccination strategies against pandemic influenza, Bulletin of Mathematical Biology, 74 (2012): 958-980.
    [17] [ E. Jung,S. Lenhart,Z. Feng, Optimal control of treatments in a two-strain tuberculosis model, Discrete and Continuous Dynamical Systems -Series B, 2 (2002): 473-482.
    [18] [ N. K. Martin,P. Vickerman,G. R. Foster,S. J. Hutchinson,D. J. Goldberg,M. Hickman, Can antiviral therapy for hepatitis C reduce the prevalence of HCV among injecting drug user populations? A modeling analysis of its prevention utility, Journal of Hepatology, 54 (2011): 1137-1144.
    [19] [ R. Storn,K. Price, Differential evolution -a simple and efficient heuristic for global optimization over continuous spaces, Journal of Global Optimization, 11 (1997): 341-359.
    [20] [ R. Thimme,S. Wieland,C. Steiger,J. Ghrayeb,K. A. Reimann, CD8(+) T cells mediate viral clearance and disease pathogenesis during acute hepatitis B virus infection, J. Virol, 77 (2003): 68-76.
    [21] [ K. V. Price, R. M. Storn and J. A. Lampinen, Differential Evolution: A Practical Approach to Global Optimization, Springer-Verlag, Berlin, Heidelberg, 2005.
    [22] [ Hepatitis B Foudation, http://www.hepb.org.
  • Reader Comments
  • © 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3164) PDF downloads(623) Cited by(7)

Article outline

Figures and Tables

Figures(13)  /  Tables(1)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog