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) approximately k(-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<gamma</=3. We also find, in this approximation, the fraction of infected individuals among those with degree k for lambda close to lambda(c). We investigate via computer simulation the contact process on a heterogeneous regular lattice and compare the results with those obtained from mean-field theory with and without neglect of degree-degree correlations.