Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Mathematical analysis of an HBV model with antibody and spatial heterogeneity

1 Department of Natural Science in the Center for General Education, Chang Gung University, Guishan, Taoyuan 333, Taiwan
2 Community Medicine Research Center, Chang Gung Memorial Hospital, Keelung Branch, Keelung 204, Taiwan
3 Department of Nursing, Chang Gung University of Science and Technology, Taoyuan City 333, Taiwan
4 Institute of Molecular Biology, Academia Sinica, Taipei 115, Taiwan
5 Liver Research Unit, Chang Gung Memorial Hospital, Keelung Branch, Keelung 204, Taiwan
6 College of Medicine, Chang Gung University, Guishan, Taoyuan 333, Taiwan

Special Issues: Spatial dynamics for epidemic models with dispersal of organisms and heterogenity of environment

In this paper, we modify the HBV model proposed in [1] to include the spatial variations of free antibody, virus-antibody complexes, and free virus. By using comparison arguments and theory of uniform persistence, we can show that the persistene/extinction of HBV can be determined by the reproduction number(s).
  Article Metrics

Keywords HBV; antibody; spatial heterogeneity; uniform persistence; reproduction number

Citation: Kuo-Sheng Huang, Yu-Chiau Shyu, Chih-Lang Lin, Feng-Bin Wang. Mathematical analysis of an HBV model with antibody and spatial heterogeneity. Mathematical Biosciences and Engineering, 2020, 17(2): 1820-1837. doi: 10.3934/mbe.2020096


  • 1. S. M. Ciupe, R. M. Ribeiro, A. S. Perelson, Antibody responses during hepatitis B viral infection, PLOS Comput. Biol., 10 (2014), e1003730.
  • 2. L. G. Guidotti, M. Isogawa, F. V. Chisari, Host-virus interactions in hepatitis B virus infection, Curr. Opin. Immunol., 36 (2015), 61-66.
  • 3. S. Bonhoeffer, R. M. May, G. M. Shaw, M. A. Nowak, Virus dynamics and drug therapy, Proc. Natl. Acad. Sci. USA, 94 (1997), 6971-6976.
  • 4. M. A. Nowak, S. Bonhoeffer, A. M. Hill, R. Boehme, H. C. Thomas, Viral dynamics in hepatitis B virus infection, Proc. Natl. Acad. Sci. USA, 93 (1996), 4398-4402.
  • 5. A. S. Perelson, D. E. Kirschner, R. de Boer, Dynamics of HIV infection of CD4 T cells, Math. Biosci., 114 (1993), 81-125.
  • 6. A. S. Perelson, P. W. Nelson, Mathematical analysis of HIV-I dynamics in vivo, SIAM Rev., 41 (1999), 3-44.
  • 7. A. S. Perelson, A. U. Neumann, M. Markowitz, J. M. Leonard, D. D. Ho, HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time, Science, 271 (1996), 1582-1586.
  • 8. S. M. Ciupe, R. M. Ribeiro, P. W. Nelson, G. Dusheiko, A. S. Perelson, The role of cells refractory to productive infection in acute hepatitis B viral dynamics, Proc. Natl. Acad. Sci. USA, 104 (2007), 5050-5055.
  • 9. S. M. Ciupe, R. M. Ribeiro, A. S. Perelson, Modeling the mechanisms of acute hepatitis B virus infection, J. Theor. Biol., 247 (2007), 23-35.
  • 10. A. Kandathil, F. Graw, J. Quinn, H. Hwang, M. Torbenson, A. Perelson, et al., Use of laser capture microdissection to map hepatitis C virus-positive hepatocytes in human liver, Gastroenterol, 145 (2013), 1404-1413.
  • 11. X. Ren, Y. Tian, L. Liu, X. Liu, A reaction-diffusion within-host HIV model with cell-to-cell transmission, J. Math. Biol., 76 (2018), 1831-1872.
  • 12. W. Wang, T. Zhang, Caspase-1-Mediated Pyroptosis of the predominance for driving CD4+ T cells death: a nonlocal spatial mathematical model, Bull. Math. Biol., 80 (2018), 540-582.
  • 13. X.-Q. Zhao, Dynamical Systems in Population Biology, second edition, Springer, New York, 2017.
  • 14. T. W. Hwang, F.-B. Wang, Dynamics of a dengue fever transmission model with crowding effect in human population and spatial variation, Discrete Cont Dyn-B, 18 (2013), 147-161.
  • 15. Y. Lou, X.-Q. Zhao, A reaction-diffusion malaria model with incubation period in the vector population, J. Math. Biol., 62 (2011), 543-568.
  • 16. R. Martin, H. L. Smith, Abstract functional differential equations and reaction-diffusion systems, Trans. Amer. Math. Soc., 321 (1990), 1-44.
  • 17. H. L. Smith, Monotone Dynamical Systems:An Introduction to the Theory of Competitive and Cooperative Systems, Math. Surveys Monogr 41, American Mathematical Society Providence, RI, 1995.
  • 18. H. C. Li, R. Peng, F.-B. Wang, Varying Total Population Enhances Disease Persistence: Qualitative Analysis on a Diffusive SIS Epidemic Model, J. Differ. Equations, 262 (2017), 885-913.
  • 19. J. Hale, Asymptotic behavior of dissipative systems, American Mathematical Society Providence, RI, 1988.
  • 20. W.-M. Ni, The mathematics of diffusion, CBMS-NSF Regional Conference Series in Applied Mathematics, 82. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2011.
  • 21. W. Wang, X.-Q. Zhao, Basic reproduction numbers for reaction-diffusion epidemic models, SIAM J. Appl. Dyn. Syst., 11 (2012), 1652-1673.
  • 22. P. van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
  • 23. O. Diekmann, J. A. P. Heesterbeek, J. A. J. Metz, On the definition and the computation of the basic reproduction ratio R0 in the models for infectious disease in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.
  • 24. H. R. Thieme, Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity, SIAM J. Appl. Math., 70 (2009), 188-211.
  • 25. M. H. Protter, H. F. Weinberger, Maximum Principles in Differential Equations, Springer-Verlag, 1984.
  • 26. H. L. Smith, X.-Q. Zhao, Robust persistence for semidynamical systems, Nonlinear Anal., 47 (2001), 6169-6179.
  • 27. P. Magal, X.-Q. Zhao, Global attractors and steady states for uniformly persistent dynamical systems, SIAM J. Math. Anal., 37 (2005), 251-275.
  • 28. H. R. Thieme, Convergence results and a Poincare-Bendixson trichotomy for asymptotically autonomous differential equations, J. Math. Biol., 30 (1992), 755-763.


This article has been cited by

  • 1. Vladimir P. Zhdanov, Joshua A. Jackman, Analysis of the initiation of viral infection under flow conditions with applications to transmission in feed, Biosystems, 2020, 104184, 10.1016/j.biosystems.2020.104184

Reader Comments

your name: *   your email: *  

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved