Many real-world networks are comprised of several networks interconnected with each other and they may have different topologies and epidemic dynamics. The dynamical behaviors of various epidemic models on coupled networks have attracted great attentions. For instance, many people adhere to the statutory working and rest days, which results in a periodic fluctuation of disease transmission in the population, and the strength of connections between two individuals cannot be ignored either. In this paper, we explore the disease transmission on weighted interconnected networks by establishing a model that includes contact strengths and periodic incidence rates. The weights on the links indicate the familiarity or intimacy of the interactive individuals. Here, we analyze the stability of the disease-free periodic solution and the unique positive periodic solution (i.e., disease-free equilibrium and endemic equilibrium) of the model, and an explicit expression for the basic reproduction number in some special cases of the periodic model is derived. We also perform numerical simulations to validate and supplement the theoretical results. It is found that the weight exponent promotes the epidemic transmission by enlarging the basic reproduction number, and the influence of internal infectious rate on epidemic prevalence is larger than that of cross infectious rate for different network structures. It is expected that this work can deepen the understanding of transmission dynamics on weighted interconnected networks.

中文翻译：

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加权互连网络上周期性流行病模型的传播动力学

许多现实世界的网络由多个相互连接的网络组成，它们可能具有不同的拓扑结构和流行动态。各种流行病模型在耦合网络上的动态行为引起了人们的极大关注。例如，很多人遵守法定的工作日和休息日，导致人群中疾病传播的周期性波动，两个人之间的联系强度也不容忽视。在本文中，我们通过建立一个包括接触强度和周期性发病率的模型来探索加权互连网络上的疾病传播。链接上的权重表示交互个体的熟悉程度或亲密程度。这里，我们分析了模型的无病周期解和唯一正周期解（即无病平衡和地方病平衡）的稳定性，在周期模型的一些特殊情况下基本再生数的显式表达式为衍生的。我们还进行数值模拟以验证和补充理论结果。发现权重指数通过扩大基本再生数促进疫情传播，对于不同的网络结构，内部传染率对流行率的影响大于交叉传染率。预计这项工作可以加深对加权互连网络传输动态的理解。并推导出周期模型某些特殊情况下基本再生数的显式表达式。我们还进行数值模拟以验证和补充理论结果。发现权重指数通过扩大基本再生数促进疫情传播，对于不同的网络结构，内部传染率对流行率的影响大于交叉传染率。预计这项工作可以加深对加权互连网络传输动态的理解。并推导出周期模型某些特殊情况下基本再生数的显式表达式。我们还进行数值模拟以验证和补充理论结果。发现权重指数通过扩大基本再生数促进疫情传播，对于不同的网络结构，内部传染率对流行率的影响大于交叉传染率。预计这项工作可以加深对加权互连网络传输动态的理解。发现权重指数通过扩大基本繁殖数促进疫情传播，对于不同的网络结构，内部传染率对流行率的影响大于交叉传染率。预计这项工作可以加深对加权互连网络传输动态的理解。发现权重指数通过扩大基本再生数促进疫情传播，对于不同的网络结构，内部传染率对流行率的影响大于交叉传染率。预计这项工作可以加深对加权互连网络传输动态的理解。