  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).
