144
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Consistent discrete global dynamics of a general initial boundary value problem for hepatitis B virus infection with capsids and adaptive immunity

ORCID Icon & ORCID Icon
Pages 777-852 | Received 05 Oct 2021, Accepted 21 May 2022, Published online: 10 Jun 2022

References

  • R.P. Beasley, C.C. Lin, K.Y. Wang, F.J. Hsieh, L.Y. Hwang, C.E. Stevens, T.S. Sun, and W. Szmuness, Hepatocellular carcinoma and hepatitis B virus, Lancet. 2 (1981), pp. 1129–1133.
  • J.R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency, J. Animal Ecol. 44 (1975), pp. 331–340.
  • N.F. Britton, Essential Mathematical Biology, Springer-Verlag, London, 2003.
  • S.M. Ciupe, R.M. Ribeiro, P.W. Nelson, and A.S. Perelson, Modeling the mechanisms of acute hepatitis B virus infection, J. Theor. Biol. 247 (2007), pp. 23–35.
  • D.L. DeAngelis, R.A. Goldstein, and R.V. O'Neill, A model for trophic interaction, Ecology. 56 (1975), pp. 881–892.
  • A.M. Elaiw, Global stability analysis of humoral immunity virus dynamics model including latently infected cells, J. Biol. Dyn. 9 (2015), pp. 215–228.
  • A.M. Elaiw and A.D. AL Agha, Global dynamics of a general diffusive HBV infection model with capsids and adaptive immune response, Adv. Differ. Equ. 2019 (2019), pp. 488–519.
  • A.M. Elaiw and N.H. AlShamrani, Global stability of humoral immunity virus dynamics models with nonlinear infection rate and removal, Nonlinear Anal. RWA. 26 (2015), pp. 161–190.
  • Y. Geng, J. Xu, and J. Hou, Discretization and dynamic consistency of a delayed and diffusive viral infection model, Appl. Math. Comput. 316 (2018), pp. 282–295.
  • S.A. Gourley, Y. Kuang, and J.D. Nagy, Dynamics of a delay differential equation model of hepatitis B virus infection, J. Biol. Dyn. 2 (2008), pp. 140–153.
  • L.G. Guidotti and F.V. Chisari, Immunobiology and pathogenesis of viral hepatitis, Annu. Rev. Pathol. Mech. Dis. 1 (2006), pp. 23–61.
  • T. Guo, H. Liu, C. Xu, and F. Yan, Global stability of a diffusive and delayed HBV infection model with HBV DNA-containing capsids and general incidence rate, Discrete Contin. Dyn. Syst. 23 (2018), pp. 4223–4242.
  • J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.
  • S. Harroudi, A. Meskaf, and K. Allali, Modelling the adaptive immune response in HBV infection model with HBV DNA Containing capsids, Differ. Equ. Dyn. Syst. (2020), doi: 10.1007/s12591-020-00549-1.
  • K. Hattaf and N. Yousfi, Global properties of a discrete viral infection model with general incidence rate, Math. Methods Appl. Sci. 39 (2016), pp. 998–1004.
  • D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, Vol. 840, Springer-Verlag, Berlin, New York, 1981.
  • C. Kang, H. Miao, X. Chen, J. Xu, and D. Huang, Global stability of a diffusive and delayed virus dynamics model with Crowley-Martin incidence function and CTL immune response, Adv. Differ. Equ.2017 (2017), pp. 324–340.
  • A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol. 66 (2004), pp. 879–883.
  • X. Li, Y. Wang, and Y. Chen, Cellular immune response in patients with chronic hepatitis B virus infection, Micro. Patho. 74 (2014), pp. 59–62.
  • K. Manna, Dynamics of a delayed diffusive HBV infection model with capsids and CTL immune response, Int. J. Appl. Comput. Math. 4 (2018), pp. 100–116.
  • K. Manna and S.P. Chakrabarty, Global stability and a non-standard finite difference scheme for a diffusion driven HBV model with capsids, J. Differ. Equ. Appl. 21 (2015), pp. 918–933.
  • K. Manna and K. Hattaf, Spatiotemporal dynamics of a generalized HBV infection model with capsids and adaptive immunity, Int. J. Appl. Comput. Math. 5 (2019), pp. 36–65.
  • H. Miao, Z. Teng, X. Abdurahman, and Z. Li, Global stability of a diffusive and delayed virus infection model with general incidence function and adaptive immune response, Comput. Appl. Math. 37 (2018), pp. 3780–3805.
  • M A Nowak, S Bonhoeffer, A M Hill, R Boehme, H C Thomas, and H McDade, Viral dynamics in hepatitis B virus infection, Proc. Natl. Acad. Sci. USA 93 (1996), pp. 4398–4402.
  • A. Pazzy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
  • M.H. Protter and H.F. Weinberger, Maximum Principles in Differential Equations, Prentice Hall, Englewood Cliffs, 1967.
  • W. Qin, L. Wang, and X. Ding, A non-standard finite difference method for a hepatitis B virus infection model with spatial diffusion, J. Differ. Equ. Appl. 20 (2014), pp. 1641–1651.
  • W. Shaoli, F. Xinlong, and H. Yinnian, Global asymptotical properties for a diffused HBV infection model with CTL immune response and nonlinear incidence, Acta Math. Sci. 31 (2011), pp. 1959–1967.
  • J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer, Berlin, 1983.
  • C. Tadmon and S. Foko, Modeling and mathematical analysis of an initial boundary value problem for hepatitis B virus infection, J. Math. Anal. Appl. 474 (2019), pp. 309–350.
  • C. Tadmon and S. Foko, Non-standard finite difference method applied to an initial boundary value problem describing hepatitis B virus infection, J. Differ. Equ. Appl. 26 (2020), pp. 122–139.
  • J.M. Vierling, The immunology of hepatitis B, Clin. Liver Dis. 11 (2007), pp. 727–759.
  • K. Wang and W. Wang, Propagation of HBV with spatial dependence, Math. Biosci. 210 (2007), pp. 78–95.
  • WHO, Hepatitis B: Fact sheet: No. 204. 2015. Available at: http://www.who.int/mediacentre/factsheets/fs204/en/.
  • R. Xu and Z. Ma, An HBV model with diffusion and time-delay, J. Theor. Biol. 257 (2009), pp. 499–509.
  • J. Xu1, J. Hou, Y. Geng, and S. Zhang, Dynamic consistent NSFD scheme for a viral infection model with cellular infection and general nonlinear incidence, Adv. Differ. Equ. 2018 (2018), pp. 108–125.
  • Y. Zhang and Z. Xu, Dynamics of a diffusive HBV model with delayed Beddington DeAngelis response, Nonlinear Anal. Real World Appl. 15 (2014), pp. 118–139.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.