Global behaviours of an in-host viral model with general incidence terms

ABSTRACT

This paper aims to investigate the global behaviours of a diffusive viral model with spatial heterogeneity on the general bounded domain and general incidence function. On the basis of the theory of uniform persistence, we obtain the system is uniformly persistent under appropriate conditions. By constructing Lyapunov functions and using LaSalle invariance principle for PDEs, we obtain that the global behaviours is completely determined by the value of the basic reproduction number for viral infection in the special case. Some numerical simulations are carried out to illustrate the analytical predictions.

Keywords:

• Viral model
• diffusion
• global attractivity

AMS Subject Classifications:

• 35B40
• 35K57
• 92D25

Acknowledgements

The authors thank two anonymous referees for very helpful comments which greatly improve the manuscript.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by National Natural Science Foundation of China [grant number 11371111]; Research Fund for the Program of Heilongjiang Bayi Agricultural University [grant number XZR2015-13].