Universality of SIS epidemics starting from small initial conditions

Dániel Keliger

Physica A: Statistical Mechanics and its Applications, 2024, vol. 644, issue C

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).

Keywords: SIS proces; Graphons; Mean field approximation; Epidemic model; Large networks (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:644:y:2024:i:c:s0378437124003522

DOI: 10.1016/j.physa.2024.129843

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