Universality of SIS epidemics starting from small initial conditions

TL;DR

This paper demonstrates that deterministic SIS epidemic models on large networks exhibit universal behavior from small initial infections, with epidemic curves converging regardless of initial infection distribution.

Contribution

It establishes the universality of epidemic trajectories starting from small initial conditions across various SIS models, including NIMFA and IMFA.

Findings

Epidemic curves become nearly identical from small initial infections.

The limit object is an eternal solution connecting disease-free and endemic states.

Framework applies to multiple benchmark SIS models.

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).