Abstract
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.
Highlights
The resilience of epidemics here means that the spreading of epidemics recovers after various perturbations
After adding the “control” stage, the simulation results on different types of networks show that the epidemic can restore to the original steady state in the finite network size under certain conditions
To observe the processes of epidemic transmission on real networks, Facebook network, Internet, and social network are examined with the SIS epidemic model, respectively
Summary
We study the resilience of epidemics on networks, by introducing a different infection rate k2 during SIS (susceptible-infected-susceptible) epidemic propagation to model perturbations (control state), whereas the infection rate is k1 in the rest of time. Through simulations and theoretical analysis, we find that even for k2 < kc, 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 $ da. We perform studies on the resilience of epidemics on networks by lowering the infection rate during control state. The discovery of cdmax can provide advanced indicator for the resilience of epidemics, which can help to design protection strategy keeping systems from a secondary epidemic outbreaks
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