Front dynamics in fractional-order epidemic models
(2011) Journal of Theoretical Biology — Vol. 279, n° 1, p. 9-16 (2011)
Files
HanertSchumacherDeleersnijder_JTB.pdf
Restricted Access - Adobe PDF
- 514.36 KB
Details
- Authors
- 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.
- Affiliations
Citations
Hanert, E., Schumacher, E., & Deleersnijder, E. (2011). Front dynamics in fractional-order epidemic models. Journal of Theoretical Biology, 279(1), 9-16. https://doi.org/10.1016/j.jtbi.2011.03.012 (Original work published 2011)