Threshold and quasi-stationary distribution for the SIS model on networks
This work provides a more accurate analytical method for studying epidemic spread on networks, which is important for epidemiologists and network scientists.
The authors improve the pair approximation for the SIS model on networks by dynamically expanding the state space to include memory of when nodes became susceptible, yielding highly accurate predictions for the epidemic threshold and quasi-stationary infection fraction on finite and infinite random graphs.
We study the Susceptible-Infectious-Susceptible (SIS) model on arbitrary networks. The well-established pair approximation treats neighboring pairs of nodes exactly while making a mean field approximation for the rest of the network. We improve the method by expanding the state space dynamically, giving nodes a memory of when they last became susceptible. The resulting approximation is simple to implement and appears to be highly accurate, both in locating the epidemic threshold and in computing the quasi-stationary fraction of infected individuals above the threshold, for both finite graphs and infinite random graphs.