102 citations · 207 across the 7 of their papers we have counts for
8 papers · 1 filter
Learning differential equation models from stochastic agent-based model simulations
John T. Nardini, Ruth E. Baker, Matthew J. Simpson +1
Agent-based models provide a flexible framework that is frequently used for modelling many biological systems, including cell migration, molecular dynamics, ecology, and epidemiolo…
Shock-fronted travelling waves in a reaction-diffusion model with nonlinear forward-backward-forward diffusion
Yifei Li, Peter van Heijster, Matthew J. Simpson +1
Reaction-diffusion equations (RDEs) are often derived as continuum limits of lattice-based discrete models. Recently, a discrete model which allows the rates of movement, prolifera…
Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media
Matthew J Simpson, Alexander P Browning, Christopher Drovandi +3
We compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is mode…
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…
Biologically-informed neural networks guide mechanistic modeling from sparse experimental data
John H. Lagergren, John T. Nardini, Ruth E. Baker +2
Biologically-informed neural networks (BINNs), an extension of physics-informed neural networks [1], are introduced and used to discover the underlying dynamics of biological syste…
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…