Susceptible‐infected‐recovered models with natural birth and death on complex networks. (27th December 2013) - Huang, Qian; Min, Lequan; Chen, Xiao
<x xml:space="preserve">Abstract</x> 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 value <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2qt16qgt" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />R˜0</alternatives> is given. It is proved that if the threshold value <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2qt16qjx" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />R˜0</alternatives> of 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.