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Universality of SIS epidemics starting from small initial conditions

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  • Keliger, Dániel

Abstract

We are investigating deterministic SIS dynamics on large networks starting from only a few infected individuals. Under mild assumptions we show that any two epidemic curves – on the same network and with the same parameters – are almost identical up to time translation when initial conditions are small enough, regardless of how infections are distributed at the beginning. The limit object – an epidemic starting from the infinite past with infinitesimally small prevalence – is identified as the nontrivial eternal solution connecting the disease free state with the endemic equilibrium. Our framework covers several benchmark models including the N-Intertwined Mean Field Approximation (NIMFA) and the Inhomogeneous Mean Field Approximation (IMFA).

Suggested Citation

  • Keliger, Dániel, 2024. "Universality of SIS epidemics starting from small initial conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 644(C).
    • Handle: RePEc:eee:phsmap:v:644:y:2024:i:c:s0378437124003522
    DOI: 10.1016/j.physa.2024.129843
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    References listed on IDEAS

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    1. Keliger, Dániel & Horváth, Illés & Takács, Bálint, 2022. "Local-density dependent Markov processes on graphons with epidemiological applications," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 324-352.
    2. Alexander Aurell & René Carmona & Gökçe Dayanıklı & Mathieu Laurière, 2022. "Finite State Graphon Games with Applications to Epidemics," Dynamic Games and Applications, Springer, vol. 12(1), pages 49-81, March.
    3. Keliger, Dániel & Horváth, Illés, 2023. "Accuracy criterion for mean field approximations of Markov processes on hypergraphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
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