Criticality in epidemics: The mathematics of sandpiles explains uncertainty in epidemic outbreaks

Abstract

We have described epidemic processes near criticality, and have given analysis for mean field models under homogeneous mixing conditions. In one case we found that an epidemiological system evolves on its own towards criticality, hence self-organizes itself towards the critical state. For spatial systems we have presented the basic description of the master equation and have shown the connection with the previous sections under the explicit analysis of mean field assumptions. A complete analysis of the spatial system would reveal qualitatively the same behaviour, in particular again power laws for the distributions of epidemics, but with different exponents. The detailed analysis via renormalization is still under debate. criticality,self organized © 2005 Springer Science + Business Media, Inc.