Global stability of the virus dynamics model with Crowley-Martin functional response

• Main Author: Shenghu Xu
• Format: Article
• Language: English
• Published: University of Szeged 2012-01-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: virus dynamics model; crowley-martin functional response; lyapunov function; stability
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=1118

In this paper, a virus dynamics model with Crowley-Martin functional response of the infection rate is investigated. By analyzing the corresponding characteristic equations, the local stability of an infection-free equilibrium point and infection equilibrium point are discussed. By constructing suitable Lyapunov functions and using LaSalles invariance principle, the global stability also are established, it is proved that if the basic reproductive number, $R_0$, is less than or equal to one, the infection-free equilibrium point is globally asymptotically stable, if $R_0$, is more than one, the infection equilibrium point is globally asymptotically stable.