Yang Junyuan, Chen Yuming, Xu Fei
Complex Systems Research Center, Shanxi University, Taiyuan, 030006, Shanxi, People's Republic of China.
School of Mathematics, Shanxi University, Taiyuan, 030006, Shanxi, People's Republic of China.
J Math Biol. 2016 Nov;73(5):1227-1249. doi: 10.1007/s00285-016-0991-7. Epub 2016 Mar 23.
In this paper, based on an SIS model, we construct an epidemic model with infection age to investigate the disease transmission on complex networks. By analyzing the characteristic equations associated with the equilibria, we obtain the basic reproduction number [Formula: see text]. It is shown that if [Formula: see text] then the disease-free equilibrium is globally asymptotically stable while if [Formula: see text] then there is a unique endemic equilibrium, which is asymptotically stable. Our investigation indicates that if the maximal degree of the network is large enough then the endemic equilibrium always exists. Sensitivity analysis on the basic reproduction number [Formula: see text] in terms of the parameters is carried out to illustrate their effects on the disease transmission and to develop appropriate control strategies.
在本文中，基于一个SIS模型，我们构建了一个带有感染年龄的流行病模型，以研究复杂网络上的疾病传播。通过分析与平衡点相关的特征方程，我们得到了基本再生数[公式：见原文]。结果表明，如果[公式：见原文]，则无病平衡点是全局渐近稳定的，而如果[公式：见原文]，则存在唯一的地方病平衡点，它是渐近稳定的。我们的研究表明，如果网络的最大度足够大，那么地方病平衡点总是存在的。对基本再生数[公式：见原文]关于参数进行了敏感性分析，以说明它们对疾病传播的影响，并制定适当的控制策略。
