In the past few decades, the frequency of pandemics has been increased due to the growth of urbanization and mobility among countries. Since a disease spreading in one country could become a pandemic with a potential worldwide humanitarian and economic impact, it is important to develop models to estimate the probability of a worldwide pandemic. In this paper, we propose a model of disease spreading in a structural modular complex network (having communities) and study how the number of bridge nodes $n$ that connect communities affects disease spread. We find that our model can be described at a global scale as an infectious transmission process between communities with global infectious and recovery time distributions that depend on the internal structure of each community and $n$. We find that near the critical point as $n$ increases, the disease reaches most of the communities, but each community has only a small fraction of recovered nodes. In addition, we obtain that in the limit $n\to \infty$, the probability of a pandemic increases abruptly at the critical point. This scenario could make the decision on whether to launch a pandemic alert or not more difficult. Finally, we show that link percolation theory can be used at a global scale to estimate the probability of a pandemic since the global transmissibility between communities has a weak dependence on the global recovery time.

中文翻译：

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流行病在模块化网络上传播：担心宣布大流行

在过去的几十年中，由于城市化和国家间流动性的增长，大流行的频率有所增加。由于在一个国家中传播的疾病可能会成为可能对全球造成人道主义和经济影响的大流行，因此开发模型来估计全球大流行的可能性非常重要。在本文中，我们提出了一种在结构模块化复杂网络（具有社区）中传播疾病的模型，并研究了桥节点的数量$ñ$连接社区会影响疾病传播。我们发现我们的模型可以在全球范围内描述为社区之间的传染传播过程，其传染性和恢复时间分布取决于每个社区的内部结构和$ñ$。我们发现在临界点附近$ñ$疾病的蔓延增加，疾病扩散到大多数社区，但是每个社区只有一小部分恢复的淋巴结。另外，在极限得到$ñ\to \infty$，在临界点大流行的可能性突然增加。这种情况可能会使是否启动大流行警报的决定变得更加困难。最后，我们证明了链接渗流理论可以在全球范围内用于估计大流行的可能性，因为社区之间的全球传播能力对全球恢复时间的依赖性很弱。