Stability preserving NSFD scheme for a delayed viral infection model with cell-to-cell transmission and general nonlinear incidence

References

• C.R.M. Bangham, The immune control and cell-to-cell spread of human T-lymphotropic virus type 1, J. Gen. Virol. 84 (2003), pp. 3177–3189.
   PubMed Web of Science ®Google Scholar
• R.M. Corless, C. Essex, and M.A.H. Nerenberg, Numerical methods can suppress chaos, Phys. Lett. A. 157 (1991), pp. 27–36.
   Web of Science ®Google Scholar
• R.V. Culshaw, S. Ruan, and G. Webb, A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay, J. Math. Biol. 46 (2003), pp. 425–444.
   PubMed Web of Science ®Google Scholar
• D.S. Dimitrov, R.L. Willey, H. Sato, L.J. Chang, R. Blumenthal, and M.A. Martin, Quantitation of human immunodeficiency virus type 1 infection kinetics, J. Virol. 67 (1993), pp. 2182–2190.
   PubMed Web of Science ®Google Scholar
• Y. Enatsu, Y. Nakata, Y. Muroya, and A. Vecchio, Global dynamics of difference equations for SIR epidemic models with a class of nonlinear incidence rates, J. Diff. Equ. Appl. 18 (2012), pp. 1163–1181.
   Web of Science ®Google Scholar
• D.F. Griffiths, P.K. Sweby, and H.C. Yee, On spurious asymptotic numerical solutions of explicit Runge-Kutta methods, IMA J. Numer. Anal. 12 (1992), pp. 319–338.
   Web of Science ®Google Scholar
• S. Gummuluru, C.M. Kinsey, and M. Emerman, An in vitro rapid-turnover assay for human immunodeficiency virus type 1 replication selects for cell-to-cell spread of virus, J. Virol. 74 (2000), pp. 10882–10891.
   PubMed Web of Science ®Google Scholar
• K. Hattaf, and N. Yousfi, A numerical method for a delayed viral infection model with general incidence rate, J. King Saud Uni. Sci. (2015).
   Google Scholar
• Z. Hu, Z. Teng, and L. Zhang, Stability and bifurcation analysis in a discrete SIR epidemic model, Math. Comput. Simulat. 97 (2014), pp. 80–93.
   Web of Science ®Google Scholar
• A. Korpusik, A nonstandard finite difference scheme for a basic model of cellular immune response to viral infection, Commun. Nonlinear. Sci. 43 (2017), pp. 369–384.
   Web of Science ®Google Scholar
• X. Lai, and X. Zou, Modeling HIV-1 virus dynamics with both virus-to-cell infection and cell-to- cell transmission, SIAM J. Appl. Math. 74 (2014), pp. 898–917.
   Web of Science ®Google Scholar
• X. Lai, and X. Zou, Modeling cell-to-cell spread of HIV-1 with logistic target cell growth, J. Math. Anal. Appl. 426 (2015), pp. 563–584.
   Web of Science ®Google Scholar
• J. Li, Z. Ma, and F. Brauer, Global analysis of discrete-time SI and SIS epidemic models, Math. Biosci. Eng. 4 (2007), pp. 699–710.
   PubMed Web of Science ®Google Scholar
• Y.F. Li, R. Xu, Z. Li, and S. Mao, Global dynamics of a delayed HIV-1 infection model with CTL immune response, Discrete. Dyn. Nat. Soc. 2011 (2011).
   Web of Science ®Google Scholar
• R.E. Mickens, Nonstandard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994.
   Google Scholar
• R.E. Mickens, Discretizations of nonlinear differential equations using explicit nonstandard methods, J. Comput. Appl. Math. 110 (1999), pp. 181–185.
   Web of Science ®Google Scholar
• R.E. Mickens, A SIR-model with square-root dynamics: An NSFD scheme, J. Diff. Equ. Appl. 16 (2010), pp. 209–216.
   Web of Science ®Google Scholar
• Y. Muroya, A. Bellen, Y. Enatsu, and Y. Nakata, Global stability for a discrete epidemic model for disease with immunity and latency spreading in a heterogeneous host population, Nonlinear Anal-Real. 13(1) (2012), pp. 258–274.
   Web of Science ®Google Scholar
• Y. Muroya, Y. Nakata, G. Izzo, and A. Vecchio, Permanence and global stability of a class of discrete epidemic models, Nonlinear Anal-Real. 12(4) (2011), pp. 2105–2117.
   Web of Science ®Google Scholar
• M.A. Nowak, and C.R.M. Bangham, Population dynamics of immune responses to persistent viruses, Science. 272 (1996), pp. 74–79.
   PubMed Web of Science ®Google Scholar
• 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. 93 (1996), pp. 4398–4402.
   PubMed Web of Science ®Google Scholar
• H. Pourbashash, S.S. Pilyugin, P. DeLeenheer, and P. De Leenheer, Global analysis of within host virus models with cell-to-cell viral transmission, Discrete Contin. Dyn. Syst. Ser. B 19 (2014), pp. 3341–3357.
   Web of Science ®Google Scholar
• M. Sekiguchi, Permanence of a discrete SIRS epidemic model with time delays, Appl. Math. Lett. 23 (2010), pp. 1280–1285.
   Web of Science ®Google Scholar
• M. Sekiguchi, and E. Ishiwata, Global dynamics of a discretized sirs epidemic model with time delay, J. Math. Anal. Appl. 371 (2010), pp. 195–202.
   Web of Science ®Google Scholar
• A. Sigal, J.T. Kim, A.B. Balazs, E. Dekel, A. Mayo, R. Milo, and D. Baltimore, Cell-to-cell spread of HIV permits ongoing replication despite antiretroviral therapy, Nature. 477 (2011), pp. 95–98.
   PubMed Web of Science ®Google Scholar
• R.P. Sigdel, and C.C. McCluskey, Global stability for an SEI model of infectious disease with immigration, Appl. Math. Comput. 243 (2014), pp. 684–689.
   Web of Science ®Google Scholar
• J. Wang, M. Guo, X. Liu, and Z. Zhao, Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay, Appl. Math. Comput. 291 (2016), pp. 149–161.
   Web of Science ®Google Scholar
• T. Wang, Z. Hu, F. Liao, and W. Ma, Global stability analysis for delayed virus infection model with general incidence rate and humoral immunity, Math. Comput. Simulat. 89 (2013), pp. 13–22.
   Web of Science ®Google Scholar
• R. Xu, Global stability of an HIV-1 infection model with saturation infection and intracellular delay, J. Math. Anal. Appl. 375(1) (2011), pp. 75–81.
   Web of Science ®Google Scholar
• J. Xu, and Y. Zhou, Bifurcation analysis of HIV-1 infectioin model with cell-to-cell transmission and immune response delay, Math. Biosci. Eng. 13 (2016), pp. 343–367.
   PubMed Web of Science ®Google Scholar
• Y. Yang, X. Ma, and Y. Li, Global stability of a discrete virus dynamics model with Holling type-II infection function, Math. Method. Appl. Sci. 39(8) (2016), pp. 2078–2082.
   Web of Science ®Google Scholar
• Y. Yang, J. Zhou, X. Ma, and T. Zhang, Nonstandard finite difference scheme for a diffusive within-host virus dynamics model with both virus-to-cell and cell-to-cell transmissions, Comput. Math. Appl. 72 (2016), pp. 1013–1020.
   Web of Science ®Google Scholar
• Y. Yang, L. Zou, and S. Ruan, Global dynamics of a delayed within-host viral infection model with both virus-to-cell and cell-to-cell transmissions, Math. Biosci. 270 (2015), pp. 183–191.
   PubMed Web of Science ®Google Scholar
• Y. Zhou, Z. Ma, and F. Brauer, A discrete epidemic model for SARS transmission and control in China, Math. Comput. Model. 40 (2004), pp. 1491–1506.
   PubMed Web of Science ®Google Scholar
• H. Zhu, and X. Zou, Impact of delays in cell infection and virus production on HIV-1 dynamics, Math. Med. Biol. 25(2) (2008), pp. 99–112.
   PubMed Web of Science ®Google Scholar
• H. Zhu, and X. Zou, Dynamics of a HIV-1 infection model with cell-mediated immune response and intracellular delay, Discrete. Contin. Dyn. Syst. Ser. B 12(2) (2009), pp. 511–524.
   Web of Science ®Google Scholar