Universality of SIS epidemics starting from small initial conditions

Dániel Keliger

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arXiv · 2204.02092

Universality of SIS epidemics starting from small initial conditions

Dániel Keliger

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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 infinitesimal 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).

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Dániel Keliger. 2022-04-05. Universality of SIS epidemics starting from small initial conditions. https://arxiv.org/abs/2204.02092

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