Pattern formation and travelling waves in a multiphase moving boundary model of tumour growth.

We employ the multiphase, moving boundary model of Byrne et al. (2003, Appl. Math.

Modelling the Effect of Matrix Metalloproteinases in Dermal Wound Healing.

With over 2 million people in the UK suffering from chronic wounds, understanding the biochemistry and pharmacology that underpins these wounds and wound healing is of high importance. Chronic wounds are characterised by high levels of matrix metalloproteinases (MMPs), which are necessary for the modification of healthy tissue in the healing process. Overexposure of MMPs, however, adversely affects healing of the wound by causing further destruction of the surrounding extracellular matrix.

Travelling-Wave and Asymptotic Analysis of a Multiphase Moving Boundary Model for Engineered Tissue Growth.

We derive a multiphase, moving boundary model to represent the development of tissue in vitro in a porous tissue engineering scaffold. We consider a cell, extra-cellular liquid and a rigid scaffold phase, and adopt Darcy's law to relate the velocity of the cell and liquid phases to their respective pressures. Cell-cell and cell-scaffold interactions which can drive cellular motion are accounted for by utilising relevant constitutive assumptions for the pressure in the cell phase.

Inhaled budesonide in the treatment of early COVID-19 (STOIC): a phase 2, open-label, randomised controlled trial.

Background: Multiple early reports of patients admitted to hospital with COVID-19 showed that patients with chronic respiratory disease were significantly under-represented in these cohorts. We hypothesised that the widespread use of inhaled glucocorticoids among these patients was responsible for this finding, and tested if inhaled glucocorticoids would be an effective treatment for early COVID-19.

Methods: We performed an open-label, parallel-group, phase 2, randomised controlled trial (Steroids in COVID-19; STOIC) of inhaled budesonide, compared with usual care, in adults within 7 days of the onset of mild COVID-19 symptoms.

Infection, inflammation and intervention: mechanistic modelling of epithelial cells in COVID-19.

While the pathological mechanisms in COVID-19 illness are still poorly understood, it is increasingly clear that high levels of pro-inflammatory mediators play a major role in clinical deterioration in patients with severe disease. Current evidence points to a hyperinflammatory state as the driver of respiratory compromise in severe COVID-19 disease, with a clinical trajectory resembling acute respiratory distress syndrome, but how this 'runaway train' inflammatory response emerges and is maintained is not known. Here, we present the first mathematical model of lung hyperinflammation due to SARS-CoV-2 infection.

Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics.

We present a solid theoretical foundation for interpreting the origin of Allee effects by providing the missing link in understanding how local individual-based mechanisms translate to global population dynamics. Allee effects were originally proposed to describe population dynamics that cannot be explained by exponential and logistic growth models. However, standard methods often calibrate Allee effect models to match observed global population dynamics without providing any mechanistic insight.

Population Dynamics with Threshold Effects Give Rise to a Diverse Family of Allee Effects.

The Allee effect describes populations that deviate from logistic growth models and arises in applications including ecology and cell biology. A common justification for incorporating Allee effects into population models is that the population in question has altered growth mechanisms at some critical density, often referred to as a threshold effect. Despite the ubiquitous nature of threshold effects arising in various biological applications, the explicit link between local threshold effects and global Allee effects has not been considered.

Accurate and efficient discretizations for stochastic models providing near agent-based spatial resolution at low computational cost.

Understanding how cells proliferate, migrate and die in various environments is essential in determining how organisms develop and repair themselves. Continuum mathematical models, such as the logistic equation and the Fisher-Kolmogorov equation, can describe the global characteristics observed in commonly used cell biology assays, such as proliferation and scratch assays. However, these continuum models do not account for single-cell-level mechanics observed in high-throughput experiments.

Emergent structures in reaction-advection-diffusion systems on a sphere.

We demonstrate unusual effects due to the addition of advection into a two-species reaction-diffusion system on the sphere. We find that advection introduces emergent behavior due to an interplay of the traditional Turing patterning mechanisms with the compact geometry of the sphere. Unidirectional advection within the Turing space of the reaction-diffusion system causes patterns to be generated at one point of the sphere, and transported to the antipodal point where they are destroyed.

Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays.

We examine the role of the travel time of a predator along a spatial network on predator-prey population interactions, where the predator is able to partially or fully sustain itself on a resource subsidy. The impact of access to food resources on the stability and behaviour of the predator-prey-subsidy system is investigated, with a primary focus on how incorporating travel time changes the dynamics. The population interactions are modelled by a system of delay differential equations, where travel time is incorporated as discrete delay in the network diffusion term in order to model time taken to migrate between spatial regions.