Threshold and quasi-stationary distribution for the susceptible-infectious-susceptible model on networks

2025/09/15 by George Cantwell, George T. Cantwell, Cristopher Moore +3 · 1 voice · 1 citation
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paper · pdf · doi:10.1103/385j-2f29

openalex publication_date 2026/04/30 · openalex created_date 2026/05/05 · openalex updated_date 2026/05/05

Abstract

We study the Susceptible-Infectious-Susceptible 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 quasistationary fraction of infected individuals above the threshold, for both finite graphs and infinite random graphs.

Citations

• A deterministic epidemic model taking account of repeated contacts between the same individuals

Cited by

• Variance of the SIS Epidemic on Networks: A Diffusion Approximation

Discussions

• We found a nice way to accurately solve the SIS model. Rather than expanding in space with ever larger moment closures (pairs, triples, ...), we expand in time. No more difficult than pair-approximati [bsky, 25 points, 2 comments]

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