Abstract Seasonal forcing and contact patterns are two key features of many disease dynamics that generate periodic patterns. Both features have not been ascertained deeply in the previous works. In this work, we develop and analyze a non-autonomous degree-based mean field network model within a Susceptible-Infected-Susceptible (SIS) framework. We assume that the disease transmission rate being periodic to study synergistic impacts of the periodic transmission and the heterogeneity of the contact network on the infection threshold and dynamics for seasonal diseases. We demonstrate both analytically and numerically that (1) the disease free equilibrium point is globally asymptotically stable if the basic reproduction number is less than one; and (2) there exists a unique global periodic solution that both susceptible and infected individuals coexist if the basic reproduction number is larger than one. We apply our framework to Scale-free contact networks for the simulation. Our results show that heterogeneity in the contact networks plays an important role in accelerating disease spreading and increasing the amplitude of the periodic steady state solution. These results confirm the need to address factors that create periodic patterns and contact patterns in seasonal disease when making policies to control an outbreak.

中文翻译：

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具有周期性感染率的网络SIS模型的动力学

摘要 季节性强迫和接触模式是许多产生周期性模式的疾病动态的两个关键特征。这两个特征在以前的作品中都没有被深入确定。在这项工作中，我们在易感-感染-易感 (SIS) 框架内开发和分析了基于非自治度的平均场网络模型。我们假设疾病传播率是周期性的，以研究周期性传播和接触网络的异质性对季节性疾病的感染阈值和动态的协同影响。我们从分析和数值上证明：（1）如果基本再生数小于 1，则无病平衡点是全局渐近稳定的；(2)如果基本繁殖数大于1，存在易感个体和感染个体共存的唯一全局周期解。我们将我们的框架应用于无标度接触网络进行模拟。我们的结果表明，接触网络中的异质性在加速疾病传播和增加周期性稳态解的幅度方面起着重要作用。这些结果证实，在制定控制爆发的政策时，需要解决在季节性疾病中产生周期性模式和接触模式的因素。我们的结果表明，接触网络中的异质性在加速疾病传播和增加周期性稳态解的幅度方面起着重要作用。这些结果证实，在制定控制爆发的政策时，需要解决在季节性疾病中产生周期性模式和接触模式的因素。我们的结果表明，接触网络中的异质性在加速疾病传播和增加周期性稳态解的幅度方面起着重要作用。这些结果证实，在制定控制爆发的政策时，需要解决在季节性疾病中产生周期性模式和接触模式的因素。