Effects of immunity on global oscillations in epidemic spreading in small-world networks

Considering a decay of an individual immunity, we investigated a susceptible-infectedrefractory-susceptible (SIRS) model in Watts-Strogatz (WS) small-word networks. It is found that when an individual immunity does not change or decays slowly in an immune period, the system can exhibit a transition from a stationary state to a large amplitude sustained oscillation. When the immunity decays rapidly in the immune period, the transition disappears and there is no oscillation. Furthermore, based on the spatio-temporal evolution patterns, it is disclosed that a long immunity period takes an important role in the emergence of the global oscillation in small world networks.