36 citations · 99 across the 6 of their papers we have counts for
7 papers
A continuum mathematical model of substrate-mediated tissue growth
Maud El-Hachem, Scott W McCue, Matthew J Simpson
We consider a continuum mathematical model of biological tissue formation inspired by recent experiments describing thin tissue growth in 3D-printed bioscaffolds. The continuum mod…
Non-vanishing sharp-fronted travelling wave solutions of the Fisher-Kolmogorov model
Maud El-Hachem, Scott W McCue, Matthew J Simpson
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…
Travelling wave analysis of cellular invasion into surrounding tissues
Maud El-Hachem, Scott W McCue, Matthew J Simpson
Single-species reaction-diffusion equations, such as the Fisher-KPP and Porous-Fisher equations, support travelling wave solutions that are often interpreted as simple mathematical…
Travelling waves, blow-up and extinction in the Fisher-Stefan model
Scott W. McCue, Maud El-Hachem, Matthew J. Simpson
While there is a long history of employing moving boundary problems in physics, in particular via Stefan problems for heat conduction accompanied by a change of phase, more recentl…
Exact sharp-fronted travelling wave solutions of the Fisher-KPP equation
Scott W McCue, Maud El-Hachem, Matthew J Simpson
A family of travelling wave solutions to the Fisher-KPP equation with speeds can be expressed exactly using Weierstrass elliptic functions. The well-known soluti…
Invading and receding sharp-fronted travelling waves
Maud El-Hachem, Scott W McCue, Matthew J Simpson
Biological invasion, whereby populations of motile and proliferative individuals lead to moving fronts that invade into vacant regions, are routinely studied using partial differen…
A sharp-front moving boundary model for malignant invasion
Maud El-Hachem, Scott W McCue, Matthew J Simpson
We analyse a novel mathematical model of malignant invasion which takes the form of a two-phase moving boundary problem describing the invasion of a population of malignant cells i…