Phase Transitions of an Epidemic Spreading Model in Small-World Networks

We propose a modified susceptible-infected-refractory-susceptible (SIRS) model to investigate the global oscillations of the epidemic spreading inWatts-Strogatz (WS) small-world networks. It is found that when an individual immunity does not change or decays slowly in an immune period, the system can exhibit complex transition from an infecting stationary state to a large amplitude sustained oscillation or an absorbing state with no infection. When the immunity decays rapidly in the immune period, the transition to the global oscillation disappears and there is no oscillation. Furthermore, based on thespatio-temporal evolution patterns and the phase diagram, it is disclosed that a long immunity period takes an important role in the emergence of the global oscillation in small-world networks.