- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Submit a Manuscript
- Table of Contents
Volume 2013 (2013), Article ID 912835, 6 pages
Optimal Antiviral Treatment Strategies of HBV Infection Model with Logistic Hepatocyte Growth
1Département de Mathématiques et Informatique, Faculté des Sciences Ben M’Sik, Université Hassan II Mohammadia, Casablanca, Morocco
2Département de Mathématiques et Informatique, Faculté des Sciences, Université Chouaib Doukkali, El Jadida, Morocco
Received 1 May 2013; Accepted 19 June 2013
Academic Editors: M. Brumen and J. R. C. Piqueira
Copyright © 2013 Hassan Laarabi 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.
- S. A. Gourley, Y. Kuang, and J. D. Nagy, “Dynamics of a delay differential model of hepatitis B virus,” Journal of Biological Dynamics, vol. 2, pp. 140–153, 2008.
- L. Min, Y. Su, and Y. Kuang, “Mathematical analysis of a basic virus infection model with application to HBV infection,” Rocky Mountain Journal of Mathematics, vol. 38, no. 5, pp. 1573–1585, 2008.
- S. Eikenberry, S. Hews, J. D. Nagy, and Y. Kuang, “The dynamics of a delay model of hepatitis B virus infection with logistic hepatocyte growth,” Mathematical Biosciences and Engineering, vol. 6, no. 2, pp. 283–299, 2009.
- 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. M. Ciupe, R. M. Ribeiro, P. W. Nelson, G. Dusheiko, and A. S. Perelson, “The role of cells refractory to productive infection in acute hepatitis B viral dynamics,” Proceedings of the National Academy of Sciences of the United States of America, vol. 104, no. 12, pp. 5050–5055, 2007.
- S. Hews, S. Eikenberry, J. D. Nagy, and Y. Kuang, “Rich dynamics of a hepatitis B viral infection model with logistic hepatocyte growth,” Journal of Mathematical Biology, vol. 60, no. 4, pp. 573–590, 2010.
- S. Lenhart and J. T. Workman, Optimal Control Applied to Biological Models, Mathematical and Computational Biology Series, Chapman & Hall/CRC, London, UK, 2007.
- W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer, New York, NY, USA, 1975.
- D. L. Lukes, Differential Equations: Classical To Controlled, vol. 162 of Math, Science and Engineering, Academic Press, New York, NY, USA, 1982.
- L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelize, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, John Wiley & Sons, New York, NY, USA, 1962.
- A. B. Gumel, P. N. Shivakumar, and B. M. Sahai, “A mathematical model for the dynamics of HIV-1 during the typical course of infection,” Nonlinear Analysis, Theory, Methods and Applications, vol. 47, no. 3, pp. 1773–1783, 2001.
- 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.
- J. Karrakchou, M. Rachik, and S. Gourari, “Optimal control and infectiology: application to an HIV/AIDS model,” Applied Mathematics and Computation, vol. 177, no. 2, pp. 807–818, 2006.
- H. Laarabi, E. Labriji, M. Rachik, and A. Kaddar, “Optimal control of an epidemic model with a saturated incidence rate,” Nonlinear Analysis: Modelling and Control, vol. 17, no. 4, pp. 448–459, 2012.