Abstracts 2024/25
Abstracts Term 1
7 October 2024: Francesca Scarabel (University of Leeds)
Title: Numerical methods for structured population models in ecology and epidemiology
Abstract: In this talk I will consider mathematical models for populations where individual rates are completely determined by a continuous structuring variable that evolves in time (e.g. age or size in ecology, age or age of infection in epidemiology). They can be described as renewal equations or partial differential equations of transport type, and the set of software tools available for these types of equations is much more limited compared to that available for compartmental models formulated as ordinary differential equations (ODEs). In recent years, within a collaboration with the University of Udine (Italy), I have developed a series of user-friendly numerical methods to study the stability and bifurcations of structured population models by means of a convenient approximation with ODEs, which can be studied with well-established software for ODEs. More recently, similar numerical techniques have been used to obtain an efficient method to approximate the reproduction numbers. I will illustrate the methods with applications to mathematical ecology and epidemiology.
14 October 2024: Emma Davis (University of Warwick)
Title: Applications of branching processes to disease emergence and elimination
21 October 2024: Denis Patterson (University of Durham)
Title: Spatial models of forest-savanna bistability
Abstract: Empirical studies suggest that for vast tracts of land in the tropics, closed-canopy forests and savannas are alternative stable states, a proposition with far-reaching implications in the context of ongoing climate change. Consequently, numerous spatially implicit and explicit mathematical models have been proposed to capture the mechanistic basis of this bistability and quantify the stability of these ecosystems. We present an analysis of a spatially extended version of the so-called Staver-Levin model of forest-savanna dynamics (a system of nonlinear partial integro-differential equations). On a homogeneous domain, we uncover various types of pattern-forming bifurcations in the presence of resource limitation, which we study as a function of the resource constraints and length scales in the problem. On larger (continental) spatial scales, heterogeneity plays a significant role in determining observed vegetative cover. Incorporating domain heterogeneity leads to interesting phenomena such as front-pinning, complex waves, and extensive multi-stability, which we investigate analytically and numerically.
28 October 2024: Anne Skeldon (University of Surrey)
Title: Mathematical modelling of the sleep-wake cycle: light, clocks and digital-twins
Abstract: We all sleep. But what determines when and for how long? In this talk I’ll describe some of the fundamental mechanisms that regulate sleep. I’ll introduce the nonsmooth coupled oscillator systems that form the basis of current mathematical models of sleep-wake regulation and discuss their dynamical behaviour. I will describe how we are using models to unravel environmental, societal and physiological factors that determine sleep timing and outline how constructing digital-twins could enable us to create personalised light interventions for sleep timing disorders.
4 November 2024: Xander O'Neill (Heriot-Watt University)
Title: Pathogen persistence in wildlife populations
Abstract: How do highly virulent pathogens persist? We start by delving into the dynamics of African swine fever, a highly virulent pathogen, which can be sustained in a wild boar population despite a mortality rate of 90-100%. How does this persist? How could the introduction of this virus impact other, more chronic illnesses, such us tuberculosis? Can the lack of control for one make it easier to control or eradicate the other? This comes full circle when we propose a more general study, asking the question, what key model characteristics lead to slower (or faster) approximate times to extinction?
11 November 2024: Laura Wadkin (Newcastle University)
Title: Modelling the spread of tree diseases and invasive pests through UK treescapes
Abstract: The loss of biodiversity due to the spread of destructive tree diseases and invasive pests within our native forests is having an enormous environmental, economic, and social impact. In the ‘25 Year Environment Plan’ the UK government highlights enhancing biosecurity as a key priority, through the control of existing diseases and pests, and by building forest resilience against new ones. We are working in collaboration with Defra to develop mathematical models to deepen our understanding of the fundamental behaviours of key pests and pathogens, act as predictive tools for forecasting, and to explore different control strategies. Broadly, we use a combination of partial differential equations, agent-based modelling, and statistical inference techniques. In this talk I will give an overview of the collaborative work to date and present a case study example of the oak processionary moth epidemic in London parks to show how the parameters for a compartmental SIR model with a time varying infection rate can be inferred.
18 November 2024: Weini Huang (Queen Mary University of London)
Title: Mathematical models of extra-chromosomal DNA and their applications in cancer
Abstract: Many diseases in human including cancers are caused by genetic alternations/errors starting from a single cell. The origin of these genetic errors and the expansion of the abnormal cells carrying these genetic errors are often stochastic processes. Here we develop a general framework to model the dynamics of cancer cells carrying extra-chromosomal DNA (ecDNA), a genetic error found in more than 30% of tumour samples across various cancer types and correlated to the worse clinical outcomes. Different from chromosomal DNA where genetic materials are on average equally divided to daughter cells controlled by centromeres during mitosis, the segregation of ecDNA copies is random partition and leads to a fast accumulation of cell-to-cell heterogeneity in copy numbers. We use deterministic and stochastic approaches to analyse the fraction of cells carrying ecDNA and copy number distributions, and use those distributions observed in experimental and clinical data to infer the selection strength of ecDNA positive cells. We further extend our model of a single ecDNA species where all ecDNA copies are identical in genetic structure and function, to multiple ecDNA types where ecDNA copies can have different genes (species), mutations (genotypes), or have different functions without genetic changes (phenotypes). All these variations of our basic model can be applied to relevant biological context and provide insight to understand ecDNA dynamics observed in clinic or experiments and improve treatment strategies.
25 November 2024: Caroline Trotter (University of Cambridge)
Title: Defeating Meningitis by 2030: how can modelling help?
Abstract: The World Health Organisation has developed an ambitious roadmap to Defeat Meningitis by 2030. The use of vaccines is key to reducing the burden of disease due to meningitis, particularly the most common forms of bacterial meningitis. A key goal is to eliminate epidemics of meningitis, which occur periodically but irregularly, in the African meningitis belt. I will describe how modelling can be used in support of the roadmap, particularly in providing evidence for vaccine policy and epidemic response.
2 December 2024: Nardus Mollentze (University of Glasgow)
Title: TBC
Abstract:
TBC