This paper is an introductory review of the problem of front propagation into unstable states.
Our presentation is centered around the concept of the asymptotic linear spreading velocity …

The dynamic behaviour of epithelial cell sheets plays a central role during development,
growth, disease and wound healing. These processes occur as a result of cell adhesion …

Biologically-informed neural networks (BINNs), an extension of physics-informed neural
networks, are introduced and used to discover the underlying dynamics of biological …

Tissue growth in bioscaffolds is influenced significantly by pore geometry, but how this
geometric dependence emerges from dynamic cellular processes such as cell proliferation …

Collective migration of eukaryotic cells plays a fundamental role in tissue growth, wound
healing and immune response. The motion, arising spontaneously or in response to …

A mathematical model is proposed to simulate the hepatitis B virus (HBV) infection with
spatial dependence. The existence of traveling waves is established via the geometric …

We investigate methods for learning partial differential equation (PDE) models from spatio-
temporal data under biologically realistic levels and forms of noise. Recent progress in …

A continuum model and a discrete model are developed to capture the population-scale and
cell-scale behavior in a wound-healing cell migration assay created from a scrape wound in …

Scratch assays are difficult to reproduce. Here we identify a previously overlooked source of
variability which could partially explain this difficulty. We analyse a suite of scratch assays in …

The Fisher–Kolmogorov–Petrovsky–Piskunov model, also known as the Fisher–KPP model,
supports travelling wave solutions that are successfully used to model numerous invasive …