Anomalous Transport of Infectious Diseases in Structured Populations

Structural properties of populations strongly influence dynamic transport and interaction such as the transmission of infectious diseases. In this paper a hierarchical block model is investigated, that schematically describes the configuration of social communities. It is shown that these models can produce super-diffusive spread and that the balance between intra- and inter-community contacts is a suitable factor for controlling the expression of this feature. The qualitative characteristics of epidemics simulated with this model are reproduced in numerical simulations of a basic fractional-in-space differential equation SIR model. Based on a stochastic formulation of the block structure, a preliminary connection between both models can be derived. The results of this paper confirm that certain structural characteristics of interacting populations can be simulated in aggregated models by employing fractional derivatives.