The study of contagion dynamics in multilayer networks has become a hot topic. Networks have the characteristics of community structure. In this work, we present a comprehensive epidemic spreading model in multilayer networks with community structure. We consider the effects of population mobility, natural mortality and natural birth rate on population dynamics and contagion dynamics. The population size is determined by natural mortality and natural birth rate. The global and local epidemic thresholds are obtained. We analyze the factors which affect epidemic thresholds. The population mobility has no effect on the global epidemic threshold, but it can affect epidemic thresholds of each community. To control outbreaks of epidemics in influential communities can well control the spreading of diseases in the whole system. It is conductive to controlling outbreak of epidemics by reducing the internal average degree and interconnected links in influential communities. Numerical simulations on synthetic networks further support and enrich our conclusions.

中文翻译：

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具有社区结构的多层网络中的传染动力学

多层网络中的传染动力学研究已成为热门话题。网络具有社区结构的特点。在这项工作中，我们提出了一个具有社区结构的多层网络中的综合流行病传播模型。我们考虑了人口流动、自然死亡率和自然出生率对人口动态和传染动态的影响。人口规模由自然死亡率和自然出生率决定。获得全局和局部流行阈值。我们分析了影响流行阈值的因素。人口流动对全球流行阈值没有影响，但会影响每个社区的流行阈值。在有影响力的社区控制流行病的爆发，可以很好地控制整个系统的疾病传播。通过降低影响社区的内部平均程度和相互关联的联系，有利于控制流行病的爆发。合成网络的数值模拟进一步支持和丰富了我们的结论。