Zheng Qianqian, Shen Jianwei, Xu Yong, Pandey Vikas, Guan Linan
School of Science, Xuchang University, Xuchang, Henan 461000, China.
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, Shaanxi, China.
Physica A. 2022 Oct 1;603:127765. doi: 10.1016/j.physa.2022.127765. Epub 2022 Jun 19.
The diffusion of the susceptible and infected is a vital factor in spreading infectious diseases. However, the previous SIR networks cannot explain the dynamical mechanism of periodic behavior and endemic diseases. Here, we incorporate the diffusion and network effect into the SIR model and describes the mechanism of periodic behavior and endemic diseases through wavenumber and saddle-node bifurcation. We also introduce the standard network structured entropy (NSE) and demonstrate diffusion effect could induce the saddle-node bifurcation and Turing instability. Then we reveal the mechanism of the periodic outbreak and endemic diseases by the mean-field method. We provide the Turing instability condition through wavenumber in this network-organized SIR model. In the end, the data from COVID-19 authenticated the theoretical results.
易感染者和感染者的扩散是传染病传播的一个关键因素。然而，先前的SIR网络无法解释周期性行为和地方病的动力学机制。在此，我们将扩散和网络效应纳入SIR模型，并通过波数和鞍结分岔来描述周期性行为和地方病的机制。我们还引入了标准网络结构熵（NSE），并证明扩散效应可引发鞍结分岔和图灵不稳定性。然后，我们通过平均场方法揭示周期性爆发和地方病的机制。在这个网络组织的SIR模型中，我们通过波数给出了图灵不稳定性条件。最后，来自COVID-19的数据验证了理论结果。
