Resilience of epidemics on networks

TL;DR

This paper investigates how epidemics on networks can recover from temporary control measures, revealing that the network's diameter influences the critical duration of control needed to prevent resurgence.

Contribution

It introduces a model with variable infection rates during epidemic control and establishes a quantitative relation between network diameter and epidemic resilience.

Findings

Epidemics can bounce back even if control reduces infection rate below critical threshold.

Critical control time is proportional to network diameter raised to a power.

Results can inform better epidemic mitigation strategies.

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 ${\lambda_{2}}$ during SIS (susceptible-infected-susceptible) epidemic propagation to model perturbations (control state), whereas the infection rate is ${\lambda_{1}}$ in the rest of time. Through simulations and theoretical analysis, we find that even for ${\lambda_{2}<\lambda_{c}}$, epidemics eventually could bounce back if control duration is below a threshold. This critical control time for epidemic resilience, i.e., ${cd_{max}}$ can be predicted by the diameter (${d}$) of the underlying network, with the quantitative relation ${cd_{max}\sim d^{\alpha}}$. Our findings can help to design a better mitigation strategy for epidemics.