  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.
