A mathematical framework for modeling propagation of infectious diseases with mobile individuals

In this paper, we propose a novel framework for modeling the diffusion of infectious diseases. In particular, we show that the infectious spread occurring between individuals that are capable of moving along a (possibly stochastic) digraph can be modeled through a (generally larger, yet sparser) stochastic digraph. The use of the proposed modeling framework makes available the whole spectrum of computational tools for stochastic digraphs, toward the quantitative study of epidemic spreading on complex networks. Salient examples are provided throughout the paper.