Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation

We investigate saturation effects in susceptible-infected-susceptible models of the spread of epidemics in heterogeneous populations. The structure of interactions in the population is represented by networks with connectivity distribution P(k), including scale-free (SF) networks with power law distributions P(k)similar tok(-gamma). Considering cases where the transmission of infection between nodes depends on their connectivity, we introduce a saturation function C(k) which reduces the infection transmission rate lambda across an edge going from a node with high connectivity k. A mean-field approximation with the neglect of degree-degree correlation then leads to a finite threshold lambda(c)>0 for SF networks with 2