42 citations · 123 across the 16 of their papers we have counts for
16 papers
Biological Modelling with Nonlocal Advection Diffusion Equations
Kevin J Painter, Thomas Hillen, Jonathan R Potts
The employment of nonlocal PDE models to describe biological aggregation and other phenomena has gained considerable traction in recent years. For cell populations, these methods g…
On the study of slow-fast dynamics, when the fast process has multiple invariant measures
B. D. Goddard, M. Ottobre, K. J. Painter +1
Motivated by applications to mathematical biology, we study the averaging problem for slow-fast systems, {\em in the case in which the fast dynamics is a stochastic process with mu…
Phenotype switching in chemotaxis aggregation models controls the spontaneous emergence of large densities
Kevin J Painter, Michael Winkler
We consider a phenotype-switching chemotaxis model for aggregation, in which a chemotactic population is capable of switching back and forth between a chemotaxing state (performing…
The impact of phenotypic heterogeneity on chemotactic self-organisation
Fiona R Macfarlane, Tommaso Lorenzi, Kevin J Painter
The capacity to aggregate through chemosensitive movement forms a paradigm of self-organisation, with examples spanning cellular and animal systems. A basic mechanism assumes a phe…
Trade-offs between chemotaxis and proliferation shape the phenotypic structuring of invading waves
Tommaso Lorenzi, Kevin J Painter
Chemotaxis-driven invasions have been proposed across a broad spectrum of biological processes, from cancer to ecology. The influential system of equations introduced by Keller and…
Leadership through influence: what mechanisms allow leaders to steer a swarm?
Sara Bernardi, Raluca Eftimie, Kevin J. Painter
Collective migration of cells and animals often relies on a specialised set of "leaders", whose role is to steer a population of naive followers towards some target. We formulate a…
Direction-Dependent Turning Leads to Anisotropic Diffusion and Persistence
Nadia Loy, Thomas Hillen, Kevin John Painter
Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool…
Mathematical models for cell migration: a nonlocal perspective
Li Chen, Kevin Painter, Christina Surulescu +1
We provide a review of recent advancements in nonlocal continuous models for migration, mainly from the perspective of its involvement in embryonal development and cancer invasion.…
Nonlocal and local models for taxis in cell migration: a rigorous limit procedure
Maria Krasnianski, Kevin Painter, Christina Surulescu +1
A rigorous limit procedure is presented which links nonlocal models involving adhesion or nonlocal chemotaxis to their local counterparts featuring haptotaxis and classical chemota…
Macroscopic descriptions of follower-leader systems
Sara Bernardi, Gissell Estrada-Rodriguez, Heiko Gimperlein +1
The fundamental derivation of macroscopic model equations to describe swarms based on microscopic movement laws and mathematical analyses into their self-organisation capabilities…
Mathematical models for chemotaxis and their applications in self-organisation phenomena
K. J. Painter
Chemotaxis is a fundamental guidance mechanism of cells and organisms, responsible for attracting microbes to food, embryonic cells into developing tissues, immune cells to infecti…
Space-time fractional diffusion in cell movement models with delay
Gissell Estrada-Rodriguez, Heiko Gimperlein, Kevin J. Painter +1
The movement of organisms and cells can be governed by occasional long distance runs, according to an approximate Lévy walk. For T cells migrating through chronically-infected brai…
Fractional Patlak-Keller-Segel equations for chemotactic superdiffusion
Gissell Estrada-Rodriguez, Heiko Gimperlein, Kevin J. Painter
The long range movement of certain organisms in the presence of a chemoattractant can be governed by long distance runs, according to an approximate Levy distribution. This article…
Spatio-temporal Models of Lymphangiogenesis in Wound Healing
Arianna Bianchi, Kevin J. Painter, Jonathan A. Sherratt
Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although…
A Mathematical Model for Lymphangiogenesis in Normal and Diabetic Wounds
Arianna Bianchi, Kevin J. Painter, Jonathan A. Sherratt
Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although…
Travelling waves in hybrid chemotaxis models
Benjamin Franz, Chuan Xue, Kevin J. Painter +1
Hybrid models of chemotaxis combine agent-based models of cells with partial differential equation models of extracellular chemical signals. In this paper, travelling wave properti…