ArticleProceedings. Mathematical, physical, and engineering sciences2019
Revisiting the Fisher-Kolmogorov-Petrovsky-Piskunov equation to interpret the spreading-extinction dichotomy.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 13 papers.
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13 citing papers in PubMed.
- Discrete and continuous mathematical models of sharp-fronted collective cell migration and invasion.Royal Society open science · 2024Article
- The mechanical influence of densification on epithelial architecture.PLoS computational biology · 2024Article
- Implementing measurement error models with mechanistic mathematical models in a likelihood-based framework for estimation, identifiability analysis and prediction in the life sciences.Journal of the Royal Society, Interface · 2024Review
- Concentration-Dependent Domain Evolution in Reaction-Diffusion Systems.Bulletin of mathematical biology · 2023Article
- A hitchhiker's guide to cancer models.Trends in biotechnology · 2022Review
- Revisiting Fisher-KPP model to interpret the spatial spreading of invasive cell population in biology.Heliyon · 2022Article
- ChemChaste: Simulating spatially inhomogeneous biochemical reaction-diffusion systems for modeling cell-environment feedbacks.GigaScience · 2022Article
- Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework.Proceedings. Mathematical, physical, and engineering sciences · 2022Article
- Incorporating domain growth into hybrid methods for reaction-diffusion systems.Journal of the Royal Society, Interface · 2021Article
- The formation of spreading front: the singular limit of three-component reaction-diffusion models.Journal of mathematical biology · 2021Article
- A free boundary mechanobiological model of epithelial tissues.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
- Predicting population extinction in lattice-based birth-death-movement models.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
- Mix and Match: Phenotypic Coexistence as a Key Facilitator of Cancer Invasion.Bulletin of mathematical biology · 2020Article
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5 authors.
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Abstract
The Fisher-Kolmogorov-Petrovsky-Piskunov model, also known as the Fisher-KPP model, supports travelling wave solutions that are successfully used to model numerous invasive phenomena with applications in biology, ecology and combustion theory. However, there are certain phenomena that the Fisher-KPP model cannot replicate, such as the extinction of invasive populations. The Fisher-Stefan model is an adaptation of the Fisher-KPP model to include a moving boundary whose evolution is governed by a Stefan condition. The Fisher-Stefan model also supports travelling wave solutions; however, a key additional feature of the Fisher-Stefan model is that it is able to simulate population extinction, giving rise to a
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