Fractional Diffusion Emulates a Human Mobility Network during a Simulated Disease Outbreak

Abstract

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Mobility networks facilitate the growth of populations, the success of invasive species, and the spread of communicable diseases among social animals, including humans. Disease control and elimination efforts, especially during an outbreak, can be optimized by numerical modeling of disease dynamics on transport networks. This is especially true when incidence data from an emerging epidemic is sparse and unreliable. However, mobility networks can be complex, challenging to characterize, and expensive to simulate with agent-based models. We therefore studied a parsimonious model for spatiotemporal disease dynamics based on a fractional diffusion equation. We implemented new stochastic simulations of a prototypical influenza-like infection spreading through the United States' highly-connected air travel network. We found that the national-averaged infected fraction during an outbreak is accurately reproduced by a space-fractional diffusion equation consistent with the connectivity of airports. Fractional diffusion therefore seems to be a better model of network outbreak dynamics than a diffusive model. Our fractional reaction-diffusion method and the result could be extended to other mobility networks in a variety of applications for population dynamics.

Keywords

• fractional diffusion
• disease modeling
• transport networks
• Levy flights
• power law phenomena