Percolation on heterogeneous networks as a model for epidemics.

We consider a spatial model related to bond percolation for the spread of a disease that includes variation in the susceptibility to infection. We work on a lattice with random bond strengths and show that with strong heterogeneity, i.e. a wide range of variation of susceptibility, patchiness in the spread of the epidemic is very likely, and the criterion for epidemic outbreak depends strongly on the heterogeneity. These results are qualitatively different from those of standard models in epidemiology, but correspond to real effects. We suggest that heterogeneity in the epidemic will affect the phylogenetic distance distribution of the disease-causing organisms. We also investigate small world lattices, and show that the effects mentioned above are even stronger.