Emergence of Self-Sustained Oscillations for SIRS Model on Random Networks

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.