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 λ_c, there is no resilience in the SIS model. Through simulations and theoretical analysis, we find that even for λ₂ < λ_c, epidemics eventually could bounce back if the control duration is below a threshold. This critical control time for epidemic resilience, i.e., cd_max, seems to be predicted by the diameter (d) of the underlying network, with the quantitative relation cd_max ∼ d^α. Our findings can help to design a better mitigation strategy for epidemics.