2022/04/05 by Keliger, Dániel
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Physics and Society (physics.soc-ph)
paper · doi:10.48550/arxiv.2204.02092
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).