Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China.
Shanxi Key Laboratory of Mathematical Technique and Big Data Analysis on Disease Control and Prevention, Taiyuan 030006, Shanxi, China.
Chaos. 2020 Jan;30(1):013147. doi: 10.1063/1.5135069.
Infectious diseases are a major threat to global health. Spatial patterns revealed by epidemic models governed by reaction-diffusion systems can serve as a potential trend indicator of disease spread; thus, they have received wide attention. To characterize important features of disease spread, there are two important factors that cannot be ignored in the reaction-diffusion systems. One is that a susceptible individual has an ability to recognize the infected ones and keep away from them. The other is that populations are usually organized as networks instead of being continuously distributed in space. Consequently, it is essential to study patterns generated by epidemic models with self- and cross-diffusion on complex networks. Here, with the help of a linear analysis method, we study Turing instability induced by cross-diffusion for a network organized SIR epidemic model and explore Turing patterns on several different networks. Furthermore, the influences of cross-diffusion and network structure on patterns are also investigated.
传染病是全球健康的主要威胁。由反应扩散系统控制的传染病模型所揭示的空间模式可以作为疾病传播的潜在趋势指标，因此受到广泛关注。为了描述疾病传播的重要特征，在反应扩散系统中，有两个重要因素不容忽视。一个是易感染个体有识别感染个体并远离他们的能力。另一个是人群通常组织成网络，而不是连续分布在空间中。因此，研究复杂网络上具有自扩散和交叉扩散的传染病模型所产生的模式至关重要。在这里，我们借助线性分析方法，研究了网络组织 SIR 传染病模型中交叉扩散引起的图灵不稳定性，并在几种不同的网络上探索了图灵模式。此外，还研究了交叉扩散和网络结构对模式的影响。
