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 λ decays exponentially with the number of reinfections n, saturating after n = l. We find a critical decaying rate εc(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 evidence that the upper critical dimension is d = 6, like in the SIR model, which can be mapped in ordinary percolation