Birth-jump processes and application to forest fire spotting
(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:
https://lup.lub.lu.se/record/7584943
- author
- Hillen, T. ; Greese, Bettina LU ; Martin, J. and de Vries, G.
- organization
- publishing date
- 2015
- 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
- pmid:25186246
- 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
- 2016-04-01 10:08:28
- date last changed
- 2023-01-02 01:30:11
@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}},
keywords = {{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}},
doi = {{10.1080/17513758.2014.950184}},
volume = {{9}},
year = {{2015}},
}