Reaction fronts in persistent random walks with demographic stochasticity
Authored by Massimo Cencini, Davide Vergni, Stefano Berti, Angelo Vulpiani
Date Published: 2019
DOI: 10.1103/physreve.99.012404
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Abstract
Standard reaction-diffusion systems are characterized by infinite
velocities and no persistence in the movement of individuals, two
conditions that are violated when considering living organisms. Here we
consider a discrete particle model in which individuals move following a
persistent random walk with finite speed and grow with logistic
dynamics. We show that, when the number of individuals is very large,
the individual-based model is well described by the continuous reactive
Cattaneo equation (RCE), but for smaller values of the carrying capacity
important finite-population effects arise. The effects of fluctuations
on the propagation speed are investigated both considering the RCE with
a cutoff in the reaction term and by means of numerical simulations of
the individual-based model. Finally, a more general Levy walk process
for the transport of individuals is examined and an expression for the
front speed of the resulting traveling wave is proposed.
Tags
models
movement
Wave
Advance
Schemes
Propagation
Reaction-diffusion systems