Cheng Xinxin, Wang Yi, Huang Gang
School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China.
Chaos Solitons Fractals. 2021 Dec;153:111502. doi: 10.1016/j.chaos.2021.111502. Epub 2021 Oct 30.
The risk of propagation of infectious diseases such as avian influenza and COVID-19 is generally controlled or reduced by quarantine measures. Considering this situation, a network-based SIQS (susceptible-infected-quarantined-susceptible) infectious disease model with nonmonotone incidence rate is established and analyzed in this paper. The psychological impact of the transmission of certain diseases in heterogeneous networks at high levels of infection may be characterized by the related nonmonotone incidence rate. The expressions of the basic reproduction number and equilibria of the model are determined analytically. We demonstrate in detail the uniform persistence of system and the global asymptotic stability of the disease-free equilibrium. The global attractivity of the unique endemic equilibrium is discussed by using monotone iteration technique. We obtain that the endemic equilibrium is globally asymptotically stable under certain conditions by constructing appropriate Lyapunov function. In addition, numerical simulations are performed to indicate the theoretical results.
诸如禽流感和新冠病毒等传染病的传播风险通常通过检疫措施来控制或降低。考虑到这种情况，本文建立并分析了一个具有非单调发病率的基于网络的SIQS（易感-感染-隔离-易感）传染病模型。在高水平感染情况下，某些疾病在异质网络中传播的心理影响可能由相关的非单调发病率来表征。通过解析确定了该模型的基本再生数和平衡点的表达式。我们详细证明了系统的一致持久性和无病平衡点的全局渐近稳定性。利用单调迭代技术讨论了唯一地方病平衡点的全局吸引性。通过构造适当的李雅普诺夫函数，我们得出在一定条件下地方病平衡点是全局渐近稳定的。此外，进行了数值模拟以表明理论结果。
