Time dependence of susceptible-infected-susceptible epidemics on networks with nodal self-infections

Abstract

The average fraction of infected nodes, in short the prevalence, of the Markovian ɛ-SIS (susceptible-infected-susceptible) process with small self-infection rate ɛ>0 exhibits, as a function of time, a typical "two-plateau" behavior, which was first discovered in the complete graph KN. Although the complete graph is often dismissed as an unacceptably simplistic approximation, its analytic tractability allows to unravel deeper details, that are surprisingly also observed in other graphs as demonstrated by simulations. The time-dependent mean-field approximation for KN performs only reasonably well for relatively large self-infection rates, but completely fails to mimic the typical Markovian ɛ-SIS process with small self-infection rates. While self-infections, particularly when their rate is small, are usually ignored, the interplay of nodal self-infection and spread over links may explain why absorbing processes are hardly observed in reality, even over long time intervals.