Threshold dynamics of a viral infection model with defectively infected cells

Jianquan Li; Xiaoyu Huo; Yuming Chen; Jianquan Li; Xiaoyu Huo; Yuming Chen

doi:10.3934/mbe.2022305

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 7: 6489-6503. doi: 10.3934/mbe.2022305

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Research article

Threshold dynamics of a viral infection model with defectively infected cells

1.
Department of Mathematics, Shaanxi University of Science and Technology, Xi'an, 710021, China
2.
Department of Mathematics, Wilfrid Laurier University, Waterloo, ON N2L 3C5, Canada

Received: 08 March 2022 Revised: 08 April 2022 Accepted: 19 April 2022 Published: 25 April 2022

In this paper, we investigate the global dynamics of a viral infection model with defectively infected cells. The explicit expression of the basic reproduction number of virus is obtained by using the next generation matrix approach, where each term has a clear biological interpretation. We show that the basic reproduction number serves as a threshold parameter. The virus dies out if the basic reproduction number is not greater than unity, otherwise the virus persists and the viral load eventually approaches a positive number. The result is established by Lyapunov's direct method. Our novel arguments for the stability of the infection equilibrium not only simplify the analysis (compared with some traditional ones in the literature) but also demonstrate some correlation between the two Lyapunov functions for the infection-free and infection equilibria.
- virus infection,
- basic reproduction number,
- equilibrium,
- global stability,
- Lyapunov's direct method
Citation: Jianquan Li, Xiaoyu Huo, Yuming Chen. Threshold dynamics of a viral infection model with defectively infected cells[J]. Mathematical Biosciences and Engineering, 2022, 19(7): 6489-6503. doi: 10.3934/mbe.2022305

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Abstract

In this paper, we investigate the global dynamics of a viral infection model with defectively infected cells. The explicit expression of the basic reproduction number of virus is obtained by using the next generation matrix approach, where each term has a clear biological interpretation. We show that the basic reproduction number serves as a threshold parameter. The virus dies out if the basic reproduction number is not greater than unity, otherwise the virus persists and the viral load eventually approaches a positive number. The result is established by Lyapunov's direct method. Our novel arguments for the stability of the infection equilibrium not only simplify the analysis (compared with some traditional ones in the literature) but also demonstrate some correlation between the two Lyapunov functions for the infection-free and infection equilibria.

References

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