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

Abstract

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.

Effects of social distancing and isolation on epidemic spreading modeled via dynamical density functional theory

“…When the underlying mobility network is too complex, an approximate description is useful in terms of Lêvy flights 95 . These can be incorporated into a diffusion equation by using fractional derivatives instead of ordinary derivatives.…”

“…These can be incorporated into a diffusion equation by using fractional derivatives instead of ordinary derivatives. Models with spatial or temporal fractional derivatives (but without repulsive interactions) have been applied to the spreading of diseases (including COVID-19) before 95 , 96 . Although a DDFT for particles undergoing Lêvy flights has, to the best of our knowledge, not been derived so far, similar models of the Cahn-Hilliard type 97 indicate that this should be possible.…”

Analysis and Optimal Control of Fractional-Order Transmission of a Respiratory Epidemic Model

“…Fractional diffusion mimics the human mobility network by simulating disease outbreaks [21]. Human mobility networks can smooth the spread of infectious diseases from the sidewalk to the flight route.…”

Nonlocal biased random walks and fractional transport on directed networks

“…Lévy flights in undirected networks have been explored in a series of works [18-20, 24, 25, 28, 29, 39-41], revealing that long-range displacements in undirected networks always improve the capacity to explore a network by inducing dynamically the small-world property [18,20]. Similar long-range strategies have been identified in human mobility [9], in the movement of cyclists between stations in bikesharing systems in Chicago and New York [10], in taxi trips in New York City [11] and in the infection spreading through the United States' highly-connected air travel network [42].…”