School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan, 410114, P. R. China.
College of Arts and Science, National University of Defense Technology, Changsha, Hunan, 410073, P.R. China.
Math Biosci Eng. 2019 Jun 19;16(5):5729-5749. doi: 10.3934/mbe.2019286.
In this paper, by taking full consideration of demographics, transfer from infectious to sus-ceptible and contact heterogeneity of the individuals, we construct an improved Susceptible-Infected-Removed-Susceptible (SIRS) epidemic model on complex heterogeneous networks. Using the next generation matrix method, we obtain the basic reproduction number $\mathcal{R}_0$ which is a critical value and used to measure the dynamics of epidemic diseases. More specifically, if $\mathcal{R}_0$ < 1, then the disease-free equilibrium is globally asymptotically stable; if $\mathcal{R}_0$ > 1, then there exists a unique endemic equilib-rium and the permanence of the disease is shown in detail. By constructing an appropriate Lyapunov function, the global stability of the endemic equilibrium is proved as well under some conditions. Moreover, the effects of three major immunization strategies are investigated. Finally, some numerical simulations are carried out to demonstrate the correctness and validness of the theoretical results.
在本文中，通过充分考虑人口统计学因素、从感染到易感的转移以及个体接触的异质性，我们在复杂异质网络上构建了一个改进的易感-感染-移除-易感（SIRS）传染病模型。使用下一代矩阵方法，我们得到了基本再生数$\mathcal{R}_0$，它是一个用于衡量传染病动力学的临界值。更具体地，如果$\mathcal{R}_0$<1，则无病平衡点全局渐近稳定；如果$\mathcal{R}_0$>1，则存在唯一的地方病平衡点，并详细展示了疾病的持久性。通过构造适当的李雅普诺夫函数，在一些条件下证明了地方病平衡点的全局稳定性。此外，还研究了三种主要免疫策略的效果。最后，进行了一些数值模拟以验证理论结果的正确性和有效性。
