title: Front dynamics in fractional-order epidemic models.
abstract: 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.
authors.affiliation: Université catholique de Louvain, Earth and Life Institute (ELI), Environmental Sciences, Croix du Sud 2/16, B-1348 Louvain-la-Neuve, Belgium. emmanuel.hanert@uclouvain.be
authors.forename: Emmanuel
authors.initials: E
authors.lastname: Hanert
authors.forename: Eva
authors.initials: E
authors.lastname: Schumacher
authors.forename: Eric
authors.initials: E
authors.lastname: Deleersnijder
mesh_terms: D000818:Animals; D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission*; D004058:Diffusion; D058872:Epidemics; D006801:Humans; D008954:Models, Biological; D013997:Time Factors