Front dynamics in fractional-order epidemic models

Emmanuel Hanert (1) , Eva Schumacher (2) , Eric Deleersnijder (2, 3)

1 ELI - Earth and Life Institute [Louvain-La-Neuve]
2 Institute of Mechanics
3 TECLIM - Centre Georges Lemaître for Earth and Climate Research [Louvain]

A number of recent studies suggest that human and animal mobility patterns exhibit scale-free, Lévy-flight dynamics. However, current reaction-diffusion epidemics models do not account for the superdiffusive spread of modern epidemics due to Lévy flights. We have developed a SIR model to simulate the spatial spread of a hypothetical epidemic driven by long-range displacements in the infective and susceptible populations. The model has been obtained by replacing the second-order diffusion operator by a fractional-order operator. Theoretical developments and numerical simulations show that fractional-order diffusion leads to an exponential acceleration of the epidemic's front and a power-law decay of the front's leading tail. Our results indicate the potential of fractional-order reaction-diffusion models to represent modern epidemics.

Mots clés: Fractional-order diffusion; Lévy flights; Epidemics spatial spread; Front dynamics

Domaines: Sciences du Vivant [q-bio]

Emmanuel Hanert, Eva Schumacher, Eric Deleersnijder. Front dynamics in fractional-order epidemic models. Journal of Theoretical Biology, 2011, 279 (1), pp.9. ⟨10.1016/j.jtbi.2011.03.012⟩. ⟨hal-00694284⟩