  We study the phase transition from the persistence phase to the extinction
phase for the SIRS (susceptible/ infected/ refractory/ susceptible) model of
diseases spreading on random networks. By studying temporal evolution and
synchronization parameter of this model on random networks, we find that, this
model on random networks, shows a synchronization phase in a narrow range of
very small values of clustering coefficient. This finding corroborates the
conclusion reached in Ref. [4] that, the clustering coefficient is responsible
for the emergence of the synchronization phase in the small world networks.
