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Front dynamics in fractional-order epidemic models
Emmanuel Hanert1, Eva Schumacher, Eric Deleersnijder
1Université 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
Journal of Theoretical Biology
|March 23, 2011
Summary
Modern epidemics spread faster than previously modeled due to Lévy-flight dynamics. A new fractional-order SIR model shows this superdiffusive spread accelerates epidemic fronts exponentially.
Area of Science:
- Epidemiology
- Mathematical Biology
- Complex Systems
Background:
- Human and animal movement patterns often follow Lévy-flight dynamics, characterized by scale-free, long-range displacements.
- Existing reaction-diffusion models for epidemics do not incorporate the superdiffusive nature of modern disease spread driven by these movement patterns.
Purpose of the Study:
- To develop and analyze a novel Susceptible-Infective-Recovered (SIR) model that accounts for superdiffusive epidemic spread.
- To investigate the impact of fractional-order diffusion, inspired by Lévy flights, on epidemic dynamics.
Main Methods:
- Modified a standard reaction-diffusion SIR model by replacing the traditional second-order diffusion operator with a fractional-order operator.
- Employed theoretical analysis and numerical simulations to study the spatial spread of a hypothetical epidemic under fractional diffusion.
Main Results:
- Fractional-order diffusion significantly alters epidemic spread dynamics compared to standard models.
- The model demonstrates an exponential acceleration of the epidemic's leading edge.
- A power-law decay was observed in the tail of the epidemic front, characteristic of superdiffusive processes.
Conclusions:
- Fractional-order reaction-diffusion models offer a more realistic framework for simulating modern epidemics influenced by long-range mobility.
- This approach captures the accelerated spatial spread and distinct tail behavior associated with Lévy-flight dynamics in disease transmission.
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