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→∞, 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.
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