Global stability of a discrete virus dynamics model with diffusion and general infection function

References

• D. Ding and X. Ding, Dynamic consistent non-standard numerical scheme for a dengue disease transmission model, J. Differ. Equ. Appl. 20 (2014), pp. 492–505.
   Web of Science ®Google Scholar
• D. Ding, W. Qin and X. Ding, Lyapunov functions and global stability for a discretized multigroup SIR epidemic model, Discrete Contin. Dyn. Syst. Ser. B 20 (2015), pp. 1971–1981.
   Web of Science ®Google Scholar
• A.M. Elaiw and N.H. AlShamrani, Global stability of humoral immunity virus dynamics models with nonlinear infection rate and removal, Nonlinear Anal. Real World Appl. 26 (2015), pp. 161–190.
   Web of Science ®Google Scholar
• Y. Enatsu, Y. Nakata and Y. Muroya, Global stability for a class of discrete SIR epidemic models, Math. Biosci. Eng. 7 (2010), pp. 347–361.
   PubMed Web of Science ®Google Scholar
• Y. Enatsu, Y. Nakata, Y. Muroya, G. Izzo and A. Vecchio, Global dynamics of difference equations for SIR epidemic models with a class of nonlinear incidence rates, J. Differ. Equ. Appl. 18 (2012), pp. 1163–1181.
   Web of Science ®Google Scholar
• S. Guo and W. Ma, Global behavior of delay differential equations model of HIV infection with apoptosis, Discrete Contin. Dyn. Syst. Ser. B 21 (2016), pp. 103–119.
   Web of Science ®Google Scholar
• K. Hattaf and N. Yousfi, A generalized HBV model with diffusion and two delays, Comput. Math. Appl. 69 (2015), pp. 31–40.
   Web of Science ®Google Scholar
• G. Huang, W. Ma and Y. Takeuchi, Global properties for virus dynamics model with Beddington-DeAngelis functional response, Appl. Math. Lett. 22 (2009), pp. 1690–1693.
   Web of Science ®Google Scholar
• Y. Ji, Global stability of a multiple delayed viral infection model with general incidence rate and an application to HIV infection, Math. Biosci. Eng. 12 (2015), pp. 525–536.
   PubMed Web of Science ®Google Scholar
• T. Kajiwara, T. Sasaki and Y. Takeuchi, Construction of Lyapunov functions for some models of infectious diseases in vivo: from simple models to complex models, Math. Biosci. Eng. 12 (2015), pp. 117–133.
   PubMed Web of Science ®Google Scholar
• A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol. 66 (2004), pp. 879–883.
   PubMed 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
• P.D. Leenheer and H.L. Smith, Virus dynamics: a global analysis, SIAM J. Appl. Math. 63 (2003), pp. 1313–1327.
   Web of Science ®Google Scholar
• M.Y. Li and H. Shu, Impact of intracellular delays and target-cell dynamics on in vivo viral infections, SIAM J. Appl. Math. 70 (2010), pp. 2434–2448.
   Web of Science ®Google Scholar
• J. Liu, B. Peng and T. Zhang, Effect of discretization on dynamical behavior of SEIR and SIR models with nonlinear incidence, Appl. Math. Lett. 39 (2015), pp. 60–66.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• C.C. McCluskey, Using Lyapunov functions to construct Lyapunov functionals for delay differential equations, SIAM J. Appl. Dyn. Syst. 14 (2015), pp. 1–24.
   Web of Science ®Google Scholar
• C.C. McCluskey and Y. Yang, Global stability of a diffusive virus dynamics model with general incidence function and time delay, Nonlinear Anal. Real World Appl. 25 (2015), pp. 64–78.
   Web of Science ®Google Scholar
• R.E. Mickens, Nonstandard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• H. Shu, L. Wang and J. Watmough, Global stability of a nonlinear viral infection model with infinitely distributed intracellular delays and CTL immune responses, SIAM J. Appl. Math. 73 (2013), pp. 1280–1302.
   Web of Science ®Google Scholar
• X. Song and A.U. Neumann, Global stability and periodic solution of the viral dynamics, J. Math. Anal. Appl. 329 (2007), pp. 281–297.
   Web of Science ®Google Scholar
• Z. Teng, L. Wang and L. Nie, Global attractivity for a class of delayed discrete SIRS epidemic models with general nonlinear incidence, Math. Meth. Appl. Sci. 38 (2015), pp. 4741–4759.
   Web of Science ®Google Scholar
• F. Wang, Y. Huang and X. Zou, Global dynamics of a PDE in-host viral model, Appl. Anal. 93 (2014), pp. 2312–2329.
   Web of Science ®Google Scholar
• J. Wang, J. Lang and X. Liu, Global dynamics for viral infection model with Beddington-DeAngelis functional response and an eclipse stage of infected cells, Discrete Contin. Dyn. Syst. Ser. B 20 (2015), pp. 3215–3233.
   Web of Science ®Google Scholar
• K. Wang and W. Wang, Propagation of HBV with spatial dependence, Math. Biosci. 210 (2007), pp. 78–95.
   PubMed Web of Science ®Google Scholar
• R. Xu and Z. Ma, An HBV model with diffusion and time delay, J. Theoret. Biol. 257 (2009), pp. 499–509.
   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. Meth. Appl. Sci. 39 (2016), pp. 2078–2082.
   Web of Science ®Google Scholar
• H. Yang and J. Wei, Global behaviour of a delayed viral kinetic model with general incidence rate, Discrete Contin. Dyn. Syst. Ser. B 20 (2015), pp. 1573–1582.
   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. 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.
   Web of Science ®Google Scholar