Global dynamics of a virus dynamical model with general incidence rate and cure rate

A virus dynamical model with general incidence rate and cure rate is proposed and analyzed. The system always admits a virus free equilibrium, which is shown to be globally asymptotically stable if the basic reproduction number R0⩽1 by using the method of Lyapunov function. And there is a unique end...

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Bibliographic Details
Published in:Nonlinear analysis: real world applications 2014-04, Vol.16, p.17-26
Main Authors: Tian, Yanni, Liu, Xianning
Format: Article
Language:English
Subjects:
Asymptotic properties
Cures
Dynamical systems
Incidence
Mathematical analysis
Mathematical models
Nonlinear dynamics
Nonlinearity
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Summary:A virus dynamical model with general incidence rate and cure rate is proposed and analyzed. The system always admits a virus free equilibrium, which is shown to be globally asymptotically stable if the basic reproduction number R0⩽1 by using the method of Lyapunov function. And there is a unique endemic equilibrium, which is locally asymptotically stable, if R0>1. Further, its global asymptotic stability is established by ruling out periodic solutions and using the Poincaré–Bendixson property for three dimensional competitive systems. The model and mathematical results in [K. Hattaf, N. Yousfi, A. Tridan, Mathematical analysis of a virus dynamics model with general incidence rate and cure rate, Nonlinear Anal. RWA 13 (2012) 1866–1872] are generalized.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2013.09.002