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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 712829, 9 pages
Hepatitis B Virus Dynamics: Modeling, Analysis, and Optimal Treatment Scheduling
1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Faculty of Science, Al-Azhar University (Assiut Branch), Assiut 71511, Egypt
3Department of Mathematics, Faculty of Science, King Khalid University, Abha 9004, Saudi Arabia
Received 8 December 2012; Revised 11 March 2013; Accepted 13 March 2013
Academic Editor: Manuel De la Sen
Copyright © 2013 A. M. Elaiw et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- M. A. Nowak, S. Bonhoeffer, A. M. Hill, R. Boehme, H. C. Thomas, and H. Mcdade, “Viral dynamics in hepatitis B virus infection,” Proceedings of the National Academy of Sciences of the United States of America, vol. 93, no. 9, pp. 4398–4402, 1996.
- M. A. Nowak and R. M. May, Virus Dynamic: Mathematical Principles of Immunology and Virology, Oxford University Press, Oxford, UK, 2000.
- S. M. Ciupe, R. M. Ribeiro, P. W. Nelson, and A. S. Perelson, “Modeling the mechanisms of acute hepatitis B virus infection,” Journal of Theoretical Biology, vol. 247, no. 1, pp. 23–35, 2007.
- S. R. Lewin, R. M. Ribeiro, T. Walters et al., “Analysis of hepatitis B viral load decline under potent therapy: complex decay profiles observed,” Hepatology, vol. 34, no. 5, pp. 1012–1020, 2001.
- M. Tsiang, J. F. Rooney, J. J. Toole, and C. S. Gibbs, “Biphasic clearance kinetics of hepatitis B virus from patients during adefovir dipivoxil therapy,” Hepatology, vol. 29, no. 6, pp. 1863–1869, 1999.
- L. Min, Y. Su, and Y. Kuang, “Mathematical analysis of a basic virus infection model with application to HBV infection,” The Rocky Mountain Journal of Mathematics, vol. 38, no. 5, pp. 1573–1585, 2008.
- C. Long, H. Qi, and S. H. Huang, “Mathematical modeling of cytotoxic lymphocyte-mediated immune response to hepatitis B virus infection,” Journal of Biomedicine and Biotechnology, vol. 2008, Article ID 743690, 9 pages, 2008.
- R. Qesmi, J. Wu, J. Wu, and J. M. Heffernan, “Influence of backward bifurcation in a model of hepatitis B and C viruses,” Mathematical Biosciences, vol. 224, no. 2, pp. 118–125, 2010.
- K. Wang and W. Wang, “Propagation of HBV with spatial dependence,” Mathematical Biosciences, vol. 210, no. 1, pp. 78–95, 2007.
- K. Wang, W. Wang, and S. Song, “Dynamics of an HBV model with diffusion and delay,” Journal of Theoretical Biology, vol. 253, no. 1, pp. 36–44, 2008.
- M. A. Nowak and C. R. M. Bangham, “Population dynamics of immune responses to persistent viruses,” Science, vol. 272, no. 5258, pp. 74–79, 1996.
- D. Wodarz and M. A. Nowak, “Mathematical models of HIV pathogenesis and treatment,” BioEssays, vol. 24, no. 12, pp. 1178–1187, 2002.
- M. A. Nowak, R. Anderson, M. Boerlijst, S. Bonhoeffer, R. May, and A. McMichael, “HIV-1 evolution and disease progression,” Science, vol. 274, pp. 1008–1010, 1996.
- M. A. Obaid, “Global analysis of a virus infection model with multitarget cells and distributed intracellular delays,” Life Science Journal, vol. 9, no. 4, pp. 1500–1508, 2012.
- A. M. Elaiw, “Global properties of a class of HIV models,” Nonlinear Analysis: Real World Applications, vol. 11, no. 4, pp. 2253–2263, 2010.
- A. M. Elaiw and S. A. Azoz, “Global properties of a class of HIV infection models with Beddington-DeAngelis functional response,” Mathematical Methods in the Applied Sciences, vol. 36, no. 4, pp. 383–394, 2013.
- A. M. Elaiw, I. A. Hassanien, and S. A. Azoz, “Global stability of HIV infection models with intracellular delays,” Journal of the Korean Mathematical Society, vol. 49, no. 4, pp. 779–794, 2012.
- A. M. Elaiw and M. A. Alghamdi, “Global properties of virus dynamics models with multitarget cells and discrete-time delays,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 201274, 19 pages, 2011.
- A. M. Elaiw, “Global properties of a class of virus infection models with multitarget cells,” Nonlinear Dynamics, vol. 69, no. 1-2, pp. 423–435, 2012.
- A. M. Elaiw, “Global dynamics of an HIV infection model with two classes of target cells and distributed delays,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 253703, 13 pages, 2012.
- A. U. Neumann, N. P. Lam, H. Dahari et al., “Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-α therapy,” Science, vol. 282, no. 5386, pp. 103–107, 1998.
- X. Song and A. U. Neumann, “Global stability and periodic solution of the viral dynamics,” Journal of Mathematical Analysis and Applications, vol. 329, no. 1, pp. 281–297, 2007.
- L. Wang and R. Xu, “Mathematical analysis of an improved hepatitis B virus model,” International Journal of Biomathematics, vol. 5, no. 1, Article ID 1250006, 18 pages, 2012.
- K. Wang, A. Fan, and A. Torres, “Global properties of an improved hepatitis B virus model,” Nonlinear Analysis: Real World Applications, vol. 11, no. 4, pp. 3131–3138, 2010.
- J. Pang, J. Cui, and J. Hui, “The importance of immune responses in a model of hepatitis B virus,” Nonlinear Dynamics, vol. 67, no. 1, pp. 723–734, 2012.
- W. Shaoli, F. Xinlong, and H. Yinnian, “Global asymptotical properties for a diffused HBV infection model with CTL immune response and nonlinear incidence,” Acta Mathematica Scientia B, vol. 31, no. 5, pp. 1959–1967, 2011.
- C. Vargas-De-León, “Stability analysis of a model for HBV infection with cure of infected cells and intracellular delay,” Applied Mathematics and Computation, vol. 219, no. 1, pp. 389–398, 2012.
- C. Vargas-De-Leon, “Analysis of a model for the dynamics of hepatitis B with noncytolytic loss of infected cells,” World Journal of Modelling and Simulation, vol. 8, no. 4, pp. 243–259, 2012.
- J. Li, K. Wang, and Y. Yang, “Dynamical behaviors of an HBV infection model with logistic hepatocyte growth,” Mathematical and Computer Modelling, vol. 54, no. 1-2, pp. 704–711, 2011.
- R. Xu and Z. Ma, “An HBV model with diffusion and time delay,” Journal of Theoretical Biology, vol. 257, no. 3, pp. 499–509, 2009.
- S. Zhang and Y. Zhou, “The analysis and application of an HBV model,” Applied Mathematical Modelling, vol. 36, no. 3, pp. 1302–1312, 2012.
- X. Tian and R. Xu, “Asymptotic properties of a hepatitis B virus infection model with time delay,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 182340, 21 pages, 2010.
- M. Sheikhan and S. A. Ghoreishi, “Application of covariance matrix adaptation-evolution strategy to optimal control of hepatitis B infection,” Neural Computing and Applications, 2012.
- C. L. Lai and M. F. Yuen, “The natural history and treatment of chronic hepatitis B: a critical evaluation of standard treatment criteria and end points,” Annals of Internal Medicine, vol. 147, no. 1, pp. 58–61, 2007.
- M. Sheikhan and S. A. Ghoreishi, “Antiviral therapy using a fuzzy controller optimized by modified evolutionary algorithms: a comparative study,” Neural Computing and Applications, 2012.
- K. Hattaf, M. Rachik, S. Saadi, and N. Yousfi, “Optimal control of treatment in a basic virus infection model,” Applied Mathematical Sciences, vol. 3, no. 17–20, pp. 949–958, 2009.
- D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, “Constrained model predictive control: stability and optimality,” Automatica, vol. 36, no. 6, pp. 789–814, 2000.
- A. M. Elaiw and X. Xia, “HIV dynamics: analysis and robust multirate MPC-based treatment schedules,” Journal of Mathematical Analysis and Applications, vol. 359, no. 1, pp. 285–301, 2009.
- A. M. Elaiw and A. M. Shehata, “Stability and feedback stabilization of HIV infection model with two classes of target cells,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 963864, 20 pages, 2012.
- É. Gyurkovics and A. M. Elaiw, “A stabilizing sampled-data -step receding horizon control with application to a HIV/AIDS model,” Differential Equations and Dynamical Systems, vol. 14, no. 3-4, pp. 323–352, 2006.
- R. Zurakowski and A. R. Teel, “A model predictive control based scheduling method for HIV therapy,” Journal of Theoretical Biology, vol. 238, no. 2, pp. 368–382, 2006.
- M. A. L. Caetano and T. Yoneyama, “Short and long period optimization of drug doses in the treatment of AIDS,” Anais da Academia Brasileira de Ciencias, vol. 74, no. 3, pp. 379–392, 2002.
- É. Gyurkovics and A. M. Elaiw, “Stabilization of sampled-data nonlinear systems by receding horizon control via discrete-time approximations,” Automatica, vol. 40, no. 12, pp. 2017–2028, 2004.
- A. M. Elaiw, “Multirate sampling and input-to-state stable receding horizon control for nonlinear systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 67, no. 5, pp. 1637–1648, 2007.