The impact of human mobility on the spreading of disease in a metapopulation is emphasized on interconnecting between patches, whereas the current volume of movement within the local population is usually neglected. Here, the role of internal commuters is taken into account by two means, a local transmission rate and the volume of internal commuters. Dynamic model of human mobility in the metapopulation with gravity coupling is presented. In conjunction with the disease spreading, the impact on invasion threshold and epidemic final size are analyzed. For two-patch model, we show that under fixing parameters in gravity model, the existence of invasion threshold depends on the difference of local transmission rates and the proportion of internal commuters between two patches. For a fully connected network with an identical transmission rate, the difference in patch final sizes is driven by patch distribution of internal commuters. By neglecting the effect of spatial variation in a simple core–satellite model, we show that the heterogeneity of internal commuters and gravity coupling induce a complex pattern of threshold, which depend mostly on the exponent in gravity model, and are responsible for the differences among local epidemic sizes.

中文翻译：

---

研究斑块内和斑块之间运动在疾病传播动态模型中的作用

人类流动对聚集人群中疾病传播的影响被强调在斑块之间的相互连接上，而当前当地人群中的移动量通常被忽略。在这里，内部通勤者的作用通过两种方式考虑，本地传输速率和内部通勤者的数量。提出了具有重力耦合的综合种群中人类流动性的动态模型。结合疾病传播，分析了对入侵阈值和流行最终规模的影响。对于两补丁模型，我们表明在重力模型中固定参数的情况下，入侵阈值的存在取决于本地传输速率的差异和两个补丁之间的内部通勤者比例。对于具有相同传输速率的全连接网络，补丁最终大小的差异是由内部通勤者的补丁分布驱动的。通过忽略简单核心 - 卫星模型中空间变化的影响，我们表明内部通勤者的异质性和重力耦合导致了复杂的阈值模式，该模式主要取决于重力模型中的指数，并导致之间的差异当地流行病规模。