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Threshold and quasistationary distribution for the susceptible-infectious-susceptible model on networks

George T. Cantwell1,* and Cristopher Moore2,†

  • *Contact author: gtc31@cam.ac.uk
  • †Contact author: moore@santafe.edu
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Phys. Rev. E 113, 064305 – Published 12 June, 2026

DOI: https://doi.org/10.1103/385j-2f29

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.

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Phys. Rev. E 113, 064305– Published 12 June, 2026
  • Received 24 September 2025
  • Accepted 30 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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