  Much recent empirical evidence shows that \textit{community structure} is
ubiquitous in the real-world networks. In this Letter, we propose a growth
model to create scale-free networks with the tunable strength (noted by $Q$) of
community structure and investigate the influence of community strength upon
the collective synchronization induced by SIRS epidemiological process. Global
and local synchronizability of the system is studied by means of an order
parameter and the relevant finite-size scaling analysis is provided. The
numerical results show that, a phase transition occurs at $Q_c\simeq0.835$ from
global synchronization to desynchronization and the local synchronization is
weakened in a range of intermediately large $Q$. Moreover, we study the impact
of mean degree $<k>$ upon synchronization on scale-free networks.
