Critical behavior of the SIS epidemic model with time-dependent   infection rate
  In this work we study a modified Susceptible-Infected-Susceptible (SIS) model in which the infection rate $\lambda$ decays exponentially with the number of reinfections $n$, saturating after $n=l$. We find a critical decaying rate $\epsilon_{c}(l)$ above which a finite fraction of the population becomes permanently infected. From the mean-field solution and computer simulations on hypercubic lattices we find evidences that the upper critical dimension is 6 like in the SIR model, which can be mapped in ordinary percolation. 
Nuno Crokidakis, Marcio Argollo de Menezes
physics.soc-ph cond-mat.stat-mech cs.SI q-bio.PE