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

Epidemic spreading on modular networks: The fear to declare a pandemic