Journal article
Random walk models in the life sciences: including births, deaths and local interactions
- Abstract:
- Random walks and related spatial stochastic models have been used in a range of application areas, including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing and oncology. Classical random walk models assume that all individuals in a population behave independently, ignoring local physical and biological interactions. This assumption simplifies the mathematical description of the population considerably, enabling continuum-limit descriptions to be derived and used in model analysis and fitting. However, interactions between individuals can have a crucial impact on population-level behaviour. In recent decades, research has increasingly been directed towards models that include interactions, including physical crowding effects and local biological processes such as adhesion, competition, dispersal, predation and adaptive directional bias. In this article, we review the progress that has been made with models of interacting individuals. We aim to provide an overview that is accessible to researchers in application areas, as well as to specialist modellers. We focus particularly on derivation of asymptotically exact or approximate continuum-limit descriptions and simplified deterministic models of mean-field behaviour and resulting spatial patterns. We provide worked examples and illustrative results of selected models. We conclude with a discussion of current areas of focus and future challenges.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Version of record, pdf, 1.5MB, Terms of use)
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- Publisher copy:
- 10.1098/rsif.2024.0422
Authors
+ Simons Foundation
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- Funder identifier:
- https://ror.org/01cmst727
- Grant:
- MP-SIP-00001828
+ Australian Research Council
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- Funder identifier:
- https://ror.org/05mmh0f86
- Grant:
- DP230100025
- Publisher:
- Royal Society
- Journal:
- Journal of the Royal Society Interface More from this journal
- Volume:
- 22
- Issue:
- 222
- Article number:
- 20240422
- Publication date:
- 2025-01-15
- Acceptance date:
- 2024-11-06
- DOI:
- EISSN:
-
1742-5662
- ISSN:
-
1742-5689
- Language:
-
English
- Keywords:
- Pubs id:
-
2062844
- Local pid:
-
pubs:2062844
- Deposit date:
-
2024-11-15
Terms of use
- Copyright holder:
- Plank et al
- Copyright date:
- 2025
- Rights statement:
- © 2025 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
- Licence:
- CC Attribution (CC BY)
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