Resilience of epidemics for SIS model on networks

Epidemic propagation on complex networks has been widely investigated, mostly with invariant parameters. However, the process of epidemic propagation is not always constant. Epidemics can be affected by various perturbations and may bounce back to its original state, which is considered resilient. Here, we study the resilience of epidemics on networks, by introducing a different infection rate λ2 during SIS (susceptible-infected-susceptible) epidemic propagation to model perturbations (control state), whereas the infection rate is λ1 in the rest of time. Noticing that when λ1 is below λc, there is no resilience in the SIS model. Through simulations and theoretical analysis, we find that even for λ2 < λc, epidemics eventually could bounce back if the control duration is below a threshold. This critical control time for epidemic resilience, i.e., cdmax, seems to be predicted by the diameter (d) of the underlying network, with the quantitative relation cdmax ~ dα. Our findings can help to design a better mitigation strategy for epidemics.