期刊
JOURNAL OF THEORETICAL BIOLOGY
卷 279, 期 1, 页码 9-16出版社
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jtbi.2011.03.012
关键词
Fractional-order diffusion; Levy flights; Epidemics spatial spread; Front dynamics
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.
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