Issue
Math. Model. Nat. Phenom.
Volume 16, 2021
Mathematical immunology
Article Number 5
Number of page(s) 13
DOI https://doi.org/10.1051/mmnp/2020058
Published online 08 February 2021
  1. A. Al-khedhairi, A.A. Elsadany and A. Elsonbaty, Modelling immune systems based on Atangana-Baleanu fractional derivative. Chaos Solitons Fract. 129 (2019) 25–39. [Google Scholar]
  2. M. Bachraoui, K. Hattaf and N. Yousfi, Dynamics of a fractional order HBV infection model with capsids and CTL immune response. Commun. Math. Biol. Neurosci. 6 (2019) 1–15. [Google Scholar]
  3. D. Baleanu, A. Jajarmi, S.S. Sajjadi and D. Mozyrska, A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator. Chaos 29 (2019) 083127. [Google Scholar]
  4. J.R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency. J. Anim. Ecol. 44 (1975) 331–340. [Google Scholar]
  5. A. Boukhouima, K. Hattaf and N. Yousfi, Modeling the Memory and Adaptive Immunity in Viral Infection. Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics. Springer, Cham (2019) 271–297. [Google Scholar]
  6. L.C. Cardoso, F.L.P. Dos Santos and R.F. Camargo, Analysis of fractional-order models for hepatitis B. Comput. Appl. Math. 37 (2018) 4570–4586. [Google Scholar]
  7. P.H. Crowley and E.K. Martin, Functional responses and interference within and between year classes of a dragonfly population. J. North Am. Bentholog. Soc. 8 (1989) 211–221. [Google Scholar]
  8. C.V. De-Leon, Volterra-type Lyapunov functions for fractional-order epidemic systems. Commun. Nonlinear Sci. Numer. Simul. 24 (2015) 75–85. [Google Scholar]
  9. D.L. DeAngelis, A.H. Goldstein and R.V. O’Neill, A model for trophic interaction. Ecology 56 (1975) 881–892. [Google Scholar]
  10. Y. Geng, J. Xu and J. Hou, Discretization and dynamic consistency of a delayed and diffusive viral infection model. Appl. Math. Comput. 316 (2018) 282–295. [Google Scholar]
  11. K. Hattaf and N. Yousfi, A class of delayed viral infection models with general incidence rate and adaptive immune response. Int. J. Dynam. Control 4 (2016) 254–265. [Google Scholar]
  12. K. Hattaf and N. Yousfi, Global properties of a diffusive HBV infection model with cell-to-cell transmission and three distributed delays. Disease Prevention and Health Promotion in Developing Countries. Springer, Cham (2020) 117–131. [Google Scholar]
  13. K. Hattaf, N. Yousfi and A. Tridane, Stability analysis of a virus dynamics model with general incidence rate and two delays. Appl. Math. Comput. 221 (2013) 514–521. [Google Scholar]
  14. J. Huo, H. Zhao and L. Zhu, The effect of vaccines on backward bifurcation in a fractional order HIV model. Nonlinear Anal.: Real World Appl. 26 (2015) 289–305. [Google Scholar]
  15. M. Mahrouf, K. Hattaf and N. Yousfi, Dynamics of a Stochastic Viral Infection Model with Immune Response. Math. Model. Nat. Phenom. 12 (2017) 15–32. [Google Scholar]
  16. 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) 65. [Google Scholar]
  17. 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) 918–933. [Google Scholar]
  18. K. Manna, Dynamics of a delayed diffusive HBV infection model with capsids and CTL immune response. Int. J. Appl. Comput. Math. 4 (2018) 116. [Google Scholar]
  19. K. Manna and S.P. Chakrabarty, Chronic hepatitis B infection and HBV DNA-containing capsids: modeling and analysis. Commun. Nonlinear Sci. Numer. Simul. 22 (2015) 383–395. [Google Scholar]
  20. K. Manna, Global properties of a HBV infection model with HBV DNA-containing capsids and CTL immune response. Int. J. Appl. Comput. Math. 3 (2017) 2323–2338. [Google Scholar]
  21. J.M. Murray, R.H. Purcell and S.F. Wieland, The half-life of hepatitis B virions. Hepatology 44 (2006) 1117–1121. [PubMed] [Google Scholar]
  22. J.M. Murray, S.F. Wieland, R.H. Purcell and F.V. Chisari, Dynamics of hepatitis B virus clearance in chimpanzees. Proc. Natl. Acad. Sci. USA 102 (49) (2005) 17780–17785. [Google Scholar]
  23. 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) 4398–4402. [Google Scholar]
  24. I. Petrás, Fractional derivatives, fractional integrals, fractional differential equations in matlab. In Engineering Education and Research Using MATLAB. InTech (2011). [Google Scholar]
  25. D. Riad, K. Hattaf and N. Yousfi, Dynamics of capital-labour model with Hattaf-Yousfi functional response. J. Adv. Math. Comput. Sci. 18 (2016) 1–7. [Google Scholar]
  26. S. Samuel and V. Gill, Time-fractional diffusion model on dynamical effect of dendritic cells on HIV pathogenesis. J. Comput. Methods Sci. Eng. 18 (2018) 1–20. [Google Scholar]
  27. S.M. Salman and A.M. Yousef, On a fractional-order model for HBV infection with cure of infected cells. J. Egypt. Math. Soc. 25 (2017) 445–451. [Google Scholar]
  28. R. Shi, T. Lu and C. Wang, Dynamic analysis of a fractional-order model for Hepatitis B Virus with Holling II functional response. Complexity 2019 (2019) 1–13. [Google Scholar]
  29. R. Shi, T. Lu and C. Wang, Dynamic analysis of a fractional-order delayed model for hepatitis B virus with CTL immune response. Virus Res. 277 (2020) 197841. [PubMed] [Google Scholar]
  30. K. Wang and W. Wang, Propagation of HBV with spatial dependence. Math. Biosci. 210 (2007) 78–95. [Google Scholar]
  31. X. Zhuo, Analysis of a HBV infection model with noncytolytic cure process. IEEE 6th International Conference on Systems Biology (ISB) (2012) 148–151. [Google Scholar]
  32. X. Zhou and Q. Sun, Stability analysis of a fractional-order HBV infection model. Int. J. Adv. Appl. Math. Mech. 2 (2014) 1–6. [Google Scholar]

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