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Birth-jump processes and application to forest fire spotting

Hillen, T.; Greese, Bettina LU ; Martin, J. and de Vries, G. (2015) In Journal of Biological Dynamics 9. p.104-127
Abstract
Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a nonlinear integro-differential equation. We present two different derivations of this equation, one based on a random walk approach and the other based on a two-compartmental reaction-diffusion model. In the case that the redistribution kernels are highly concentrated, we show that the integro-differential equation can be approximated by a reaction-diffusion equation, in which the proliferation rate contributes to both the diffusion term and the reaction term. We completely solve the corresponding critical domain size problem and the minimal wave speed problem. Birth-jump models can be applied in... (More)
Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a nonlinear integro-differential equation. We present two different derivations of this equation, one based on a random walk approach and the other based on a two-compartmental reaction-diffusion model. In the case that the redistribution kernels are highly concentrated, we show that the integro-differential equation can be approximated by a reaction-diffusion equation, in which the proliferation rate contributes to both the diffusion term and the reaction term. We completely solve the corresponding critical domain size problem and the minimal wave speed problem. Birth-jump models can be applied in many areas in mathematical biology. We highlight an application of our results in the context of forest fire spread through spotting. We show that spotting increases the invasion speed of a forest fire front. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
45K05, 35Q92, 92B05, wildfire spotting, minimal wave speed, critical domain size, reaction-diffusion equations, diffusion limit, integro-differential equations, birth-jump processes
in
Journal of Biological Dynamics
volume
9
pages
104 - 127
publisher
Taylor & Francis
external identifiers
  • wos:000356911600009
  • scopus:84937578055
ISSN
1751-3766
DOI
10.1080/17513758.2014.950184
language
English
LU publication?
yes
id
6401c9b2-88f4-4728-a226-b8f9f1e61958 (old id 7584943)
date added to LUP
2015-07-23 08:24:46
date last changed
2017-02-12 03:05:29
@article{6401c9b2-88f4-4728-a226-b8f9f1e61958,
  abstract     = {Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a nonlinear integro-differential equation. We present two different derivations of this equation, one based on a random walk approach and the other based on a two-compartmental reaction-diffusion model. In the case that the redistribution kernels are highly concentrated, we show that the integro-differential equation can be approximated by a reaction-diffusion equation, in which the proliferation rate contributes to both the diffusion term and the reaction term. We completely solve the corresponding critical domain size problem and the minimal wave speed problem. Birth-jump models can be applied in many areas in mathematical biology. We highlight an application of our results in the context of forest fire spread through spotting. We show that spotting increases the invasion speed of a forest fire front.},
  author       = {Hillen, T. and Greese, Bettina and Martin, J. and de Vries, G.},
  issn         = {1751-3766},
  keyword      = {45K05,35Q92,92B05,wildfire spotting,minimal wave speed,critical domain size,reaction-diffusion equations,diffusion limit,integro-differential equations,birth-jump processes},
  language     = {eng},
  pages        = {104--127},
  publisher    = {Taylor & Francis},
  series       = {Journal of Biological Dynamics},
  title        = {Birth-jump processes and application to forest fire spotting},
  url          = {http://dx.doi.org/10.1080/17513758.2014.950184},
  volume       = {9},
  year         = {2015},
}