Open AccessThreshold dynamics of a viral infection model with defectively infected cells
Author(s) -
Jianquan Li,
Xiaoyu Huo,
Yuming Chen
Publication year - 2022
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2022305
Subject(s) - viral infection , basic reproduction number , lyapunov function , biology , virus , dynamics (music) , viral matrix protein , stability (learning theory) , matrix (chemical analysis) , reproduction , virology , viral load , mathematics , expression (computer science) , biological system , computer science , physics , ecology , chemistry , population , chromatography , nonlinear system , quantum mechanics , machine learning , acoustics , demography , sociology , programming language
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.