We grew yeast biofilms on four agar densities and tracked width, cell viability and thickness. To interpret the data, we extended a thin-film model that treats the colony as a two-phase viscous fluid: a living phase that consumes nutrient and proliferates, and an inactive phase of dead cells, with cell death converting one to the other. The biofilm takes up nutrients from the agar, facilitating expansion which is resisted by biofilm–agar adhesion. Fitting five parameters (growth rate, death rate, nutrient uptake rate, nutrient consumption rate, slip coefficient) at each agar density showed that stronger adhesion was the clearest and most robust effect of increased agar density.

Soft Matter

Many natural systems involve stochastic and deterministic behaviours, but capturing both in a single representation is difficult. For example, traditional models, like Lotka-Volterra, can predict tiny, unrealistic population levels, so-called atto-type problem. This becomes an issue when studying things like species extinction, or clearance of an infection, where stochasticity plays a key role. While discrete stochastic models, e.g. continuous-time Markov chains (CTMCs), handle this properly, they are computationally slow to simulate for large systems. To address this, we developed a new framework called Jump-Switch-Flow (JSF), combining the accuracy of CTMCs with the speed of ordinary differential equation simulation. JSF allows populations to truly reach extinction, avoiding the atto-type problem. We apply our framework to several case studies, including public health intervention analysis and SARS-CoV-2 infection data. JSF is openly available as an easy-to-use Python package. Overall, JSF is a powerful new tool for realistically and efficiently modelling complex, multi-scale systems.

Journal of Mathematical Biology

The time-series susceptible-infectious-recovered (TSIR) model has been widely used to study the nonlinear dynamics of acute immunising infections. This study identifies a bias from the standard TSIR assumption that vaccination can be represented as a reduction in the recruitment of susceptible individuals, or the birth rate. When vaccination occurs after birth, individuals infected before vaccination may be double-counted during susceptible reconstruction, creating a bias in the estimation of the reporting rate and total cases. The magnitude of this bias increases with vaccination coverage. We show this bias and propose a simple correction that accounts for infections occurring before vaccination using an age-structured SIR model of measles transmission.

PLoS ONE

In this study, we use compartmental modelling and bifurcation analysis to explore how innate immune cells interact with endometrial cells during early stages of endometriosis onset. Endometriosis is a chronic condition in which cells similar to those in the uterine lining (the endometrium) grow in lesions outside of the uterus. Our findings indicate the hypothesis of increased endometrial cell presence in the pelvic cavity alone is insufficient to cause endometriosis. Rather, a reduction in immune cell cytotoxicity is a more likely cause of disease. We predict that a decline in immune function (cytotoxicity or endometrial cell detection) can result in endometriosis onset, and a significant improvement in function is then required for disease recovery, due to hysteresis in the system. This work provides a novel approach for understanding endometriosis onset.

Royal Society Interface