Threshold dynamics of a viral infection model with defectively infected cells

Mathematical Biosciences and Engineering

Jianquan Li¹  Xiaoyu Huo¹  Yuming Chen² 

[1] 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;

关键词: virus infection;    basic reproduction number;    equilibrium;    global stability;    lyapunov's direct method;   

DOI  :  10.3934/mbe.2022305

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown