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Mathematical and Computer Modelling of Dynamical Systems
Methods, Tools and Applications in Engineering and Related Sciences
Volume 30, 2024 - Issue 1
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Research Article

Structural stability of the hepatitis C model with the proliferation of infected and uninfected hepatocytes

, , , ORCID Icon &
Pages 51-72 | Received 14 Nov 2023, Accepted 08 Jan 2024, Published online: 04 Feb 2024

References

  • L.B. Seeff and J.H. Hoofnagle. 2002. National institutes of health consensus development conference: Management of hepatitis C: 2002. Hepatology. 36 (5B): S1–S2. doi: 10.1053/jhep.2002.36992.
  • A.U. Neumann, N.P. Lam, H. Dahari, D.R. Gretch, T.E. Wiley, T.J. Layden, and A.S. Perelson. 1998. Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-α therapy, Science. 282 (5386): 103–107. doi: 10.1126/science.282.5386.103.
  • H. Dahari, A. Lo, R.M. Ribeiro, and A.S. Perelson. 2007. Modeling hepatitis C virus dynamics: Liver regeneration and critical drug efficacy, J. Theor. Biol. 247 (2): 371–381. doi: 10.1016/j.jtbi.2007.03.006.
  • H. Dahari, R.M. Ribeiro, and A.S. Perelson. 2007. Triphasic decline of hepatitis C virus RNA during antiviral therapy, Hepatology 46 (1): 16–21. doi: 10.1002/hep.21657.
  • T.C. Reluga, H. Dahari, and A.S. Perelson. 2009. Analysis of hepatitis C virus infection models with hepatocyte homeostasis, SIAM J Appl Math 69 (4): 999–1023. doi: 10.1137/080714579.
  • T. Telksnys, Z. Navickas, I. Timofejeva, R. Marcinkevicius, and M. Ragulskis. 2019. Symmetry breaking in solitary solutions to the Hodgkin–Huxley model, Nonlinear Dyn 97 (1): 571–582. doi: 10.1007/s11071-019-04998-4.
  • T. Telksnys, Z. Navickas, M.A. Sanjuán, R. Marcinkevicius, and M. Ragulskis 2020. Kink solitary solutions to a hepatitis C evolution model, Discrete And Contin. Dynamical Syst.-B. 25 4427–4447.
  • Z. Navickas, R. Marcinkevicius, T. Telksnys, and M. Ragulskis. 2016. Existence of second order solitary solutions to Riccati differential equations coupled with a multiplicative term, Ima J. Appl. Math. 81 (6): 1163–1190. doi: 10.1093/imamat/hxw050.
  • J.K. Hale. 1997. Diffusive coupling, dissipation, and synchronization, J. Dyn. Differ. Equ. 9 (1): 1–52. doi: 10.1007/BF02219051.
  • M.C. Cross and P.C. Hohenberg. 1993. Pattern formation outside of equilibrium, Rev Mod Phys 65 (3): 851. doi: 10.1103/RevModPhys.65.851.
  • S.Y. Shafi, M. Arcak, M. Jovanović, and A.K. Packard 2013. Synchronization of diffusively-coupled limit cycle oscillators, Automatica 49 (12): 3613–3622. doi: 10.1016/j.automatica.2013.09.011.
  • A. Din. 2021. The stochastic bifurcation analysis and stochastic delayed optimal control for epidemic model with general incidence function, Chaos: An Interdiscip. J. Nonlinear Sci. 31 (12): doi: 10.1063/5.0063050
  • A. Din, Y. Li, A. Yusuf, J. Liu, and A.A. Aly. 2022. Impact of information intervention on stochastic hepatitis B model and its variable-order fractional network, Eur Phys J Spec Top 231 (10): 1859–1873. doi: 10.1140/epjs/s11734-022-00453-5.
  • A. Din, Y. Li, and A. Yusuf. 2021. Delayed hepatitis B epidemic model with stochastic analysis, Chaos Soliton. Fract. 146 110839. doi: 10.1016/j.chaos.2021.110839.
  • A. Din and Y. Li. 2021. Stationary distribution extinction and optimal control for the stochastic hepatitis B epidemic model with partial immunity, Phys. Scr. 96 (7): 074005. doi: 10.1088/1402-4896/abfacc.
  • A. Din and Y. Li. 2022. Mathematical analysis of a new nonlinear stochastic hepatitis B epidemic model with vaccination effect and a case study, Eur. Phys. J. Plus 137 (5): 1–24. doi: 10.1140/epjp/s13360-022-02748-x.
  • A. Din and Q.T. Ain. 2022. Stochastic optimal control analysis of a mathematical model: Theory and application to non-singular kernels, Fractal. Fract. 6 (5): 279 doi: 10.3390/fractalfract6050279.
  • A. Columbu, S. Frassu, and G. Viglialoro. 2023. Properties of given and detected unbounded solutions to a class of chemotaxis models, Stud. Appl. Math. 151 (4): 1349–1379. doi: 10.1111/sapm.12627.
  • T. Li, S. Frassu, and G. Viglialoro. 2023. Combining effects ensuring boundedness in an attraction–repulsion chemotaxis model with production and consumption, Z. Angew. Math. Phys. 74 (3): 109. doi: 10.1007/s00033-023-01976-0.
  • K. Hattaf. 2023. A new class of generalized fractal and fractal-fractional derivatives with non-singular kernels, Fractal. Fract. 7 (5): 395. doi: 10.3390/fractalfract7050395.
  • K. Hattaf. 2022. On the stability and numerical scheme of fractional differential equations with application to biology, Computation 10 (6): 97. doi: 10.3390/computation10060097.
  • A. Tridane, K. Hattaf, R. Yafia, and F.A. Rihan. 2016. Mathematical modeling of HBV with the antiviral therapy for the immunocompromised patients, Commun. Math. Biol. Neurosci 2016. Article–ID 20.
  • Scott A. 2006. Encyclopedia of Nonlinear Science. New York: Routledge.
  • J.H. He and X.H. Wu. 2006. Exp-function method for nonlinear wave equations, Chaos Soliton. Fract. 30 (3): 700–708. doi: 10.1016/j.chaos.2006.03.020.
  • Z. Navickas, L. Bikulciene, and M. Ragulskis. 2010. Generalization of Exp-function and other standard function methods, Appl. Math. Comput. 216 (8): 2380–2393. doi: 10.1016/j.amc.2010.03.083.
  • D.E. Knuth. 1992. Two notes on notation, Am. Math. Mon. 99 (5): 403–422. doi: 10.1080/00029890.1992.11995869.
  • Arnold V.I. 1988. Geometrical Methods in the Theory of Ordinary Differential Equations, Vol. 250. New York: Springer.
  • T. Nagatani. 2020. Migration difference in diffusively-coupled prey–predator system on heterogeneous graphs, Physica A 537 122705. doi: 10.1016/j.physa.2019.122705.