Unexpected epidemic thresholds in heterogeneous networks: the role of disease transmission.

We reformulate several recent analyses of infection processes on highly heterogeneous networks (e.g., scale-free networks) which conclude that diseases will spread and persist even for vanishingly small transmission probabilities. The results of these latter studies contrast with conventional epidemiological models where there are clear threshold effects, namely, should the transmission probability fall below a critical threshold level the disease is expected to die out. Here we show that epidemic propagation depends equally on the infection scheme as well as the network structure. Connectivity-dependent infection schemes can yield threshold effects even in scale-free networks where they would otherwise be unexpected.