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Susceptible‐infected‐recovered models with natural birth and death on complex networks
Author(s) -
Huang Qian,
Min Lequan,
Chen Xiao
Publication year - 2013
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.3048
Subject(s) - stability theory , mathematics , basic reproduction number , lyapunov function , epidemic model , value (mathematics) , mathematical economics , stability (learning theory) , computer science , statistics , demography , physics , population , nonlinear system , quantum mechanics , machine learning , sociology
This paper proposes two modified susceptible‐infected‐recovered (SIRS) models on homogenous and heterogeneous networks, respectively. In the study of the homogenous network model, Lyapunov functions are used to study the globally asymptotically stable of the equilibria of the model. It is proved that if the basic reproduction number of the model is less than one, then the disease‐free equilibrium is globally asymptotically stable, otherwise, the endemic equilibrium is globally asymptotically stable. In the study of the heterogeneous network model, the existences of the disease‐free equilibrium and epidemic equilibrium of the model are discussed. A threshold valueR ˜ 0is given. It is proved that if the threshold valueR ˜ 0of the model is less than one, then the disease‐free equilibrium is globally asymptotically stable. The simulation examples on the two SIRS models are given. Copyright © 2013 John Wiley & Sons, Ltd.