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- W4285666906 abstract "The Fisher-KPP model, and generalisations thereof, is a simple reaction-diffusion models of biological invasion that assumes individuals in the population undergo linear diffusion with diffusivity $D$, and logistic proliferation with rate $lambda$. Biologically-relevant initial conditions lead to long-time travelling wave solutions that move with speed $c=2sqrt{lambda D}$. Despite these attractive features, there are several biological limitations of travelling wave solutions of the Fisher-KPP model. First, these travelling wave solutions do not predict a well-defined invasion front. Second, biologically-relevant initial conditions lead to travelling waves that move with speed $c=2sqrt{lambda D} > 0$. This means that, for biologically-relevant initial data, the Fisher-KPP model can not be used to study invasion with $c ne 2sqrt{lambda D}$, or retreating travelling waves with $c < 0$. Here, we reformulate the Fisher-KPP model as a moving boundary problem on $x < s(t)$, and we show that this reformulated model alleviates the key limitations of the Fisher-KPP model. Travelling wave solutions of the moving boundary problem predict a well-defined front, and can propagate with any wave speed, $-infty < c < infty$. Here, we establish these results using a combination of high-accuracy numerical simulations of the time-dependent partial differential equation, phase plane analysis and perturbation methods. All software required to replicate this work is available on GitHub." @default.
- W4285666906 created "2022-07-17" @default.
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- W4285666906 date "2021-07-12" @default.
- W4285666906 modified "2023-09-27" @default.
- W4285666906 title "Non-vanishing sharp-fronted travelling wave solutions of the Fisher-Kolmogorov model" @default.
- W4285666906 doi "https://doi.org/10.48550/arxiv.2107.05210" @default.
- W4285666906 hasPublicationYear "2021" @default.
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