Abstract
We study the phase transition from the persistence phase to the extinction phase forthe SIRS (susceptible/ infected/ refractory/ susceptible) model of diseases spreading onrandom networks. By studying a temporal evolution and synchronization parameter ofthis model on random networks, we find that, this model on random networks, shows asynchronization phase in a narrow range of very small values of clustering coecient. This ending corroborates the conclusion reached in [Phys. Rev. Lett. 86, 2909 (2001)] that,the clustering coexocient is responsible for the emergence of the synchronization phasein the small world networks. With these results and the result that we had obtainedin [Physica A 535, 122251 (2019)], we give a reasonable justiffcation the reason for theoccurrence of that behavior, at small values of the clustering coeffcient.
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