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)∼ k^-γ . 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 λ 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 λ_c >0 for SF networks with 2<γ⩽3 . We also find, in this approximation, the fraction of infected individuals among those with degree k for λ close to λ_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.