Related papers: Fisher-KPP-type models of biological invasion: Ope…
Biological invasion, whereby populations of motile and proliferative individuals lead to moving fronts that invade into vacant regions, are routinely studied using partial differential equation (PDE) models based upon the classical…
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…
Reaction-diffusion models are often used to describe biological invasion, where populations of individuals that undergo random motility and proliferation lead to moving fronts. Many models of biological invasion are extensions of the…
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 recently such approaches have been adapted to study biological…
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 models of biological invasion. Such travelling wave…
Continuum mathematical models for collective cell motion normally involve reaction-diffusion equations, such as the Fisher-KPP equation, with a linear diffusion term to describe cell motility and a logistic term to describe cell…
The famous Fisher-KPP reaction-diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it…
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 into a population of background tissue, such as skin. Cells…
We consider a family of exact solutions to a nonlinear reaction-diffusion model, constructed using nonclassical symmetry analysis. In a particular limit, the mathematical model approaches the well-known Fisher-KPP model, which means that it…
Non-cooperative Fisher-KPP systems with space-time periodic coefficients are motivated for instance by models for structured populations evolving in periodic environments. This paper is concerned with entire solutions describing the…
Invasion waves are a fundamental building block of theoretical ecology. In this study we aim to take the first steps to link propagation failure and fast acceleration of traveling waves to critical transitions (or tipping points). The…
We investigate pattern formation in a two-dimensional (2D) Fisher--Stefan model, which involves solving the Fisher--KPP equation on a compactly-supported region with a moving boundary. By combining the Fisher--KPP and classical Stefan…
In this study, we investigate a porous medium-type flux limited reaction--diffusion equation that arises in morphogenesis modeling. This nonlinear partial differential equation is an extension of the generalized…
Real-world cellular invasion processes often take place in curved geometries. Such problems are frequently simplified in models to neglect the curved geometry in favour of computational simplicity, yet doing so risks inaccuracy in any…
We consider a minimal go-or-grow model of cell invasion, whereby cells can either proliferate, following logistic growth, or move, via linear diffusion, and phenotypic switching between these two states is density-dependent. Formal analysis…
In this paper, we treat the Fisher-KPP equation with a Caputo-type time fractional derivative and discuss the propagation speed of the solution. The equation is a mathematical model that describes the processes of sub-diffusion,…
An analysis of traveling wave solutions of partial differential equation (PDE) systems with cross-diffusion is presented. The systems under study fall in a general class of the classical Keller-Segel models to describe chemotaxis. The…
Spatio-temporal dynamics of the evolution of population involving growth and diffusion processes can be modeled by class of partial diffusion equations (PDEs) known as reaction-diffusion systems. In this work, we developed a nonlinear…
We consider a moving boundary mathematical model of biological invasion. The model describes the spatiotemporal evolution of two adjacent populations: each population undergoes linear diffusion and logistic growth, and the boundary between…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…