Fractional Diffusion Emulates a Human Mobility Network during a Simulated Disease Outbreak - Gustafson, Kyle B.; Bayati, Basil S.; Eckhoff, Philip A. (Frontiers in Ecology and Evolution, 2017)
Human mobility networks facilitate the dynamics of communicable diseases through populations. Similar processes can be observed during population growth or ecological invasion. Disease control and elimination efforts, especially during an outbreak, may depend on numerical modeling of the dynamics of disease on transport networks. However, these networks can be complex, poorly characterized and expensive to simulate at the microscale. As a proof of principle, we computationally studied a parsimonious model for spatiotemporal disease dynamics based on a generalized, or fractional, diffusion equation. We implemented new stochastic simulations of a prototypical influenza-like infection spreading through the United States' highly-connected air travel network. Remarkably, we found that the network-averaged fraction of infected individuals during an SIS outbreak, driven by air traffic in the USA, is most accurately reproduced by a space-fractional diffusion equation consistent with the geographic distribution of airports. This fractional diffusion model could therefore be used to estimate network outbreak dynamics based only on the length distribution of journeys on the network.