Fractional diffusion emulates a human mobility network during a simulated disease outbreak

TL;DR

This study demonstrates that a two-parameter space-fractional diffusion equation can accurately model the spread of a disease on the US air travel network, highlighting the importance of heavy-tailed mobility patterns.

Contribution

The paper introduces a novel application of space-fractional diffusion equations to emulate human mobility-driven disease spread on air travel networks.

Findings

Mobility on the air network follows a power-law distribution.

Fractional diffusion models replicate outbreak evolution accurately.

Parameters of the model are determined by the network structure.

Abstract

From footpaths to flight routes, human mobility networks facilitate the spread of communicable diseases. Control and elimination efforts depend on characterizing these networks in terms of connections and flux rates of individuals between contact nodes. In some cases, transport can be parameterized with gravity-type models or approximated by a diffusive random walk. As a alternative, we have isolated intranational commercial air traffic as a case study for the utility of non-diffusive, heavy-tailed transport models. We implemented new stochastic simulations of a prototypical influenza-like infection, focusing on the dense, highly-connected United States air travel network. We show that mobility on this network can be described mainly by a power law, in agreement with previous studies. Remarkably, we find that the global evolution of an outbreak on this network is accurately reproduced by a two-parameter space-fractional diffusion equation, such that those parameters are determined by the air travel network.