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Dynamical behaviors of a discrete HIV‐1 virus model with bilinear infective rate
Author(s) -
Shi Peilin,
Dong Lingzhen
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2974
Subject(s) - mathematics , lyapunov function , basic reproduction number , stability theory , discretization , virus , stability (learning theory) , bilinear interpolation , control theory (sociology) , virology , mathematical analysis , computer science , control (management) , biology , statistics , nonlinear system , physics , artificial intelligence , population , demography , quantum mechanics , machine learning , sociology
We establish a discrete virus dynamic model by discretizing a continuous HIV‐1 virus model with bilinear infective rate using ‘hybrid’ Euler method. We discuss not only the existence and global stability of the uninfected equilibrium but also the existence and local stability of the infected equilibrium. We prove that there exists a crucial value similar to that of the continuous HIV‐1 virus dynamics, which is called the basic reproductive ratio of the virus. If the basic reproductive ratio of the virus is less than one, the uninfected equilibrium is globally asymptotically stable. If the basic reproductive ratio of the virus is larger than one, the infected equilibrium exists and is locally stable. Moreover, we consider the permanence for such a system by constructing a Lyapunov function v n . Copyright © 2013 John Wiley & Sons, Ltd.