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Understanding the impact of non-linearity in the SIS model

Author

Listed:
  • Friedrich, Tobias
  • Göbel, Andreas
  • Klodt, Nicolas
  • Krejca, Martin S.
  • Pappik, Marcus

Abstract

The SIS model is a classic model from epidemiology that formalizes a variety of diffusion processes on networks, such as biological infections and information dissemination. In this model, vertices are either infected or susceptible to an infection. Infected vertices infect their neighbors independently at a rate λ>0, and each infected vertex becomes susceptible at a rate of 1. Overall, these dynamics imply that each susceptible vertex with exactly m infected neighbors becomes infected at rate λm, that is, linear in m. However, it has been observed that various processes exhibit a non-linear scaling of the infection rate with respect to m. For these kinds of processes, no fully rigorous guarantees exist so far.

Suggested Citation

  • Friedrich, Tobias & Göbel, Andreas & Klodt, Nicolas & Krejca, Martin S. & Pappik, Marcus, 2024. "Understanding the impact of non-linearity in the SIS model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 656(C).
    • Handle: RePEc:eee:phsmap:v:656:y:2024:i:c:s0378437124007180
    DOI: 10.1016/j.physa.2024.130209
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    References listed on IDEAS

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    1. Zhang, Yihui & Tang, Shaoting & Pei, Sen & Yan, Shu & Jiang, Shijin & Zheng, Zhiming, 2015. "Health behavior spreading with similar diminishing returns effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 425(C), pages 18-26.
    2. Bjarke Mønsted & Piotr Sapieżyński & Emilio Ferrara & Sune Lehmann, 2017. "Evidence of complex contagion of information in social media: An experiment using Twitter bots," PLOS ONE, Public Library of Science, vol. 12(9), pages 1-12, September.
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