Front dynamics in fractional-order epidemic models

JOURNAL OF THEORETICAL BIOLOGY

卷:279

Article

Hanert, Emmanuel¹  Schumacher, Eva²  Deleersnijder, Eric^1,2 

[1] Catholic Univ Louvain, ELI, Georges Lemaitre Ctr Earth & Climate Res TECLIM, B-1348 Louvain, Belgium

[2] Catholic Univ Louvain, Inst Mech Mat & Civil Engn, B-1348 Louvain, Belgium

关键词: Fractional-order diffusion;    Levy flights;    Epidemics spatial spread;    Front dynamics;   

DOI  :  10.1016/j.jtbi.2011.03.012

来源: Elsevier

【 摘 要 】

A number of recent studies suggest that human and animal mobility patterns exhibit scale-free, Levy-flight dynamics. However, current reaction-diffusion epidemics models do not account for the superdiffusive spread of modern epidemics due to Levy 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. (C) 2011 Elsevier Ltd. All rights reserved.

【 授权许可】

Free