arXiv subjects

Louise Dyson

Publications and source records attributed to Louise Dyson.

6 recordsLinked to original sources

arXiv2026

Early warning signals of non-critical transitions from linearised time-varying dynamics with applications to epidemic systems

In the wake of the SARS-CoV-2 pandemic, there has been heightened interest from applied mathematicians in infectious disease modelling. Modelling efforts often focus on predicting whether diseases are likely to be eliminated or, instead, (re-)emerge, especially as a result of control measures.This tipping point between elimination and infection waves has been successfully anticipated in the literature through the use of early warning signals and such signals often rely on the theory of critical slowing down. Recent developments have shown that these signals (increases in fluctuation variance and return time) can emerge from the system geometry in the case of non-normal dynamics rather than a change in asymptotic stability. We show how such dynamical behaviour occurs in the fluctuations from the mean-field in general stochastic systems. Using the susceptible-infectious-recovered model as an example application, we analyse how critical-like behaviour can be exploited to anticipate infection waves in the absence of an equilibrium bifurcation.

q-bio.PE↗

arXiv2016

Simplification and analysis of a model of social interaction in voting

A recently proposed model of social interaction in voting is investigated by simplifying it down into a version that is more analytically tractable and which allows a mathematical analysis to be performed. This analysis clarifies the interplay of the different elements present in the system --- social influence, heterogeneity and noise --- and leads to a better understanding of its properties. The origin of a regime of bistability is identified. The insight gained in this way gives further intuition into the behaviour of the original model.

physics.soc-ph↗

arXiv2016

Staged Models for Interdisciplinary Research

Modellers of complex biological or social systems are often faced with an invidious choice: to use simple models with few mechanisms that can be fully analysed, or to construct complicated models that include all the features which are thought relevant. The former ensures rigour, the latter relevance. We discuss a method that combines these two approaches, beginning with a complex model and then modelling the complicated model with simpler models. The resulting "chain" of models ensures some rigour and relevance. We illustrate this process on a complex model of voting intentions, constructing a reduced model which agrees well with the predictions of the full model. Experiments with variations of the simpler model yield additional insights which are hidden by the complexity of the full model. This approach facilitated collaboration between social scientists and physicists -- the complex model was specified based on the social science literature, and the simpler model constrained to agree (in core aspects) with the complicated model.

physics.soc-ph↗

arXiv2015

Onset of collective motion in locusts is captured by a minimal model

We present a minimal model to describe the onset of collective motion seen when a population of locusts are placed in an annular arena. At low densities motion is disordered, while at high densities locusts march in a common direction, which may reverse during the experiment. The data is well-captured by an individual-based model, in which demographic noise leads to the observed density-dependent effects. By fitting the model parameters to equation-free coefficients, we give a quantitative comparison, showing time series, stationary distributions and the mean switching times between states.

q-bio.PE↗

arXiv2015

The statistics of fixation times for systems with recruitment

We investigate the statistics of the time taken for a system driven by recruitment to reach fixation. Our model describes a series of experiments where a population is confronted with two identical options, resulting in the system fixating on one of the options. For a specific population size, we show that the time distribution behaves like an inverse Gaussian with an exponential decay. Varying the population size reveals that the timescale of the decay depends on the population size and allows the critical population number, below which fixation occurs, to be estimated from experimental data.

cond-mat.stat-mech↗

arXiv2014

Noise-Induced Bistable States and Their Mean Switching Time in Foraging Colonies

We investigate a type of bistability where noise not only causes transitions between stable states, but also constructs the states themselves. We focus on the experimentally well-studied system of ants choosing between two food sources to illustrate the essential points, but the ideas are more general. The mean time for switching between the two bistable states of the system is calculated. This suggests a procedure for estimating, in a real system, the critical population size above which bistability ceases to occur.

q-bio.PE↗