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

Abstract

In this paper, we designed and analysed a discrete model to solve a delayed within-host viral infection model by using non-standard finite difference scheme. The original model that we considered was a delayed viral infection model with cell-to-cell transmission, cell-mediated immune response and general nonlinear incidence. We show that the discrete model has equilibria which are exactly the same as those of the original continuous model and the conditions for those equilibria to be globally asymptotically stable are consistent with the original continuous model with no restriction on the time step size. The results imply that the discretization scheme can efficiently preserves the qualitative properties of solutions for corresponding continuous model.

Keywords:

• NSFD scheme
• cell-to-cell transmission
• general nonlinear incidence
• globally asymptotically stable

AMS Subject Classifications:

• 34K20
• 34K25
• 92D30

Acknowledgements

The authors wish to express their deepest gratitude to the anonymous referee and the editors for their valuable comments and suggestions, which have greatly improved this article.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11301314], [grant number 11501443], [grant number 11571272]; PhD research startup foundation of Xi’an University of Technology[grant number 109-451116017]; Innovation Technology Foundation of Xi’an University of Technology [grant number 109-451016032].