Mathematical Biology and Medicine

Jobs News


  • 12 Dec 2023 (3pm, Roger Stevens LT8) Giulia Belluccini Los Alamos
    Mathematical models of hepatitis B infection Nearly 300 million of people are chronically infected with hepatitis B virus (HBV). Currently no cure has been developed, leading to more than 800,000 HBV-related deaths annually. The focus of therapies is on eliminating the template for HBV replication, i.e. covalently closed circular DNA (cccDNA). However, HBV surface antigens (HBsAg) derive also from integrated DNA (iDNA). The presence of HBsAg activates the immune response, which leads to an inflammatory state and eventually to liver damage. Our collaborators at the Viral Hepatitis Center of John Hopkins University considered a cohort of 10 HBV-HIV co-infected participants on nucleos(t)ide analogue (NUC) therapy for a short or long time (from a few months to almost 12 years). Liver biopsies were obtained from each individual at 2 time points and single cell analysis was performed, measuring the genetic material inside each cell. First, we quantify the decay/growth of the number of cells with viral genetic material, and its timescale, with the aim of understanding how NUC therapy affects this dynamics. Then, we build a stochastic model that accounts for hepatocytes spatial distribution to study the distribution of infected cells and how the viral genetic material accumulates inside each cell.
  • 12 Dec 2023 (12 noon, Roger Stevens LT14) Luís Hernandez-Navarro Leeds
    Coupled environmental and demographic fluctuations shape the evolution of cooperative antimicrobial resistance
    The rise of antimicrobial resistance (AMR) is a global threat responsible for millions of deaths, and we therefore have a pressing need to better understand how microbial populations respond to antimicrobial drugs, and to find mechanisms to possibly eradicate AMR cells. The inactivation of antimicrobials by resistant microbes can often be viewed as a cooperative behaviour, leading to the long-lived coexistence of resistant and sensitive cells in static environments. In this talk, I will discuss how this picture is greatly altered in more realistic, volatile environments, where microbial communities commonly evolve. By combining analytical and computational means, we characterise the environmental conditions for the long-lived coexistence or extinction of each type of cells, and we unveil a novel fluctuation-driven AMR eradication mechanism, where resistant microbes experience bottlenecks leading to extinction.
  • 7 Dec 2023 Wasiur Khuda Bukhsh Nottingham
    Approximations and parameter inference for epidemic models
    In this presentation, I will talk about a recently developed method, called the dynamical survival analysis (DSA), for parameter inference of models of infectious disease epidemiology. In a nutshell, the DSA method allows us to interpret mean-filed ordinary or partial differential equations for proportions of individuals in different compartments as probabilistic quantities, such as the survival function, density etc, by virtue of an application of the Sellke construction. I will provide example applications to both network-based and mass-action models. I will discuss when those two types of models are equivalent in some precise sense, and when one class of models can be approximated by another one, e.g., an SEIR model by an SIR model.
  • 16 Nov 2023 Adrianne Jenner QUT
    Using virtual clinical trials to improve our understanding of diseases
    Mathematical and computational techniques can improve our understanding of diseases. In this talk, I'll present ways in which data from cancer patients can be combined with mathematical modelling and used to improve cancer treatments.
    Given the variability in individual responses to cancer treatments, agent-based modelling has been a useful technique for accurately capturing cellular behaviours that may lead to stochasticity in patient outcomes. Using a hybrid agent-based model and partial differential equation system, we developed a model for brain cancer (glioblastoma) growth informed by ex-vivo patient samples. Extending the model to capture patient treatment with an oncolytic virus rQNestin, we used our model to propose reasons for treatment failure, which was later confirmed with further patient samples. More recently, we extended this model to investigate the effectiveness of combination treatments (chemotherapy, virotherapy and immunotherapy) informed by individual patient imaging mass cytometry.
    This talk hopes to provide examples of ways mathematical and computational modelling can be used to run ``virtual'' clinical trials with the goal of obtaining more effective treatments for diseases.
  • 26 Oct 2023 Helena Stage Bristol
    The role of superinfection in evolutionary epidemiology
    The study of evolutionary epidemiology is vital to understand and control the spread of e.g. anti-microbial resistance, but poses serious challenges due to the multi-scale presence of the forces driving pathogen evolution. For example, selection for high within-host fitness may reduce between-host transmission. Time-since-infection models are much more flexible than ODEs in capturing aspects of both within- and between-host scales, but studying the feedback loops between such scales remains non-trivial. We will discuss how a general theory for time-since-infection models that allow for superinfection (e.g. multi-strain systems with partial cross-immunity) can capture recent infection history and quantify the system's steady states. This will be explored through a series of toy models which admit the same qualitative features as are observed in more complex model descriptions. We will distinguish between the cases when superinfection of the host facilitates the coexistence of two (or more) infections that interact synergistically by fuelling each other's spread (syndemic), and when these infections hinder each other.
  • 19 Oct 2023 Katie Link Pfizer
    Mathematical modeling of extended-release pre-exposure prophylasis and drug-resistant HIV
    The pharmacologic tail of long-acting cabotegravir (CAB-LA), an injectable Pre-Exposure Prophylaxis (PrEP), allows for months-long intervals between injections, but it may facilitate the emergence of drug-resistant human immunodeficiency virus (HIV) strains during the acute infection stage. In this study, we present a within-host, mechanistic ordinary differential equation model of the HIV latency and infection cycle in CD4+ T cells to investigate the impact of CAB-LA on drug-resistant mutations in both humans and macaques. We develop a pharmacokinetic/pharmacodynamic model for CAB-LA to correlate the inhibitory drug response with the drug concentration in plasma. After validating our model against experimental results, we conduct in-silico trials. First, we separately administer CAB-LA to the in-silico macaque and human patients prior to and post-simian-human immunodeficiency virus (SHIV)/HIV exposure, to observe SHIV and HIV infectivity dynamics, respectively. Although the model does not incorporate a mechanism for CAB-LA-induced HIV mutations, we analyze the outcomes when mutations occur naturally. Our findings suggest that CAB-LA may enhance the growth of drug-resistant strains over the wild-type strains during the acute stage. The in-silico trials demonstrate that the effectiveness of CAB-LA against mutations and the fitness of the drug-resistant strain to infect T cells determine the course of the mutated strain.
  • 5 Oct 2023 Simone De Reggi University of Udine
    A journey through structured populations: stability analysis of infinite-dimensional dynamical systems and relevant numerics
    Population dynamics are often described by means of structures, i.e., variables representing individual traits (e.g., age, size, immunity, spatial position). These models can be formulated as (integro-)partial differential equations which, as a result, lead to deal with abstract evolution equations. In this talk I will present some basic concepts on continuously structured populations, starting from the well known McKendrick-von Foerster equation. I will introduce the basic tools for the stability analysis of infinite-dimensional dynamical systems by drawing a parallel with well-known approaches for Ordinary Differential Equations (including the concept of the basic reproduction number). In the last part I will discuss some numerical methods for the stability analysis of equilibria. Numerical results attesting the validity of the approaches and applications to models from epidemiology and ecology are presented.
  • 21 Sep 2023 Mohit Kumar Jolly IISc Bangalore
    Design principles of decision-making networks in cancer cell plasticity and T cell differentiation
    Decoding the emergent dynamics of cellular differentiation is crucial in understanding how cells make decisions during development and modulate those decisions for cellular reprogramming. Decision-making is often driven by complex interconnected networks, whose design principles remain poorly understood. I will present examples from our work on CD4+ T-cell differentiation into Th1, Th2, Th17 and hybrid states, as well as from cancer cell plasticity during metastasis. These networks exhibit multistability, thus enabling cells to reversibly alter their phenotypes. Moreover, the specific dynamical features seen in these networks are largely unique to them, indicating evolutionary selection of these networks in enabling multicellularity. Analysis of transcriptomic data analysis from relevant datasets validates our model predictions, and highlight how an integration of dynamical modeling with transcriptomic data can quantitatively map the cellular decision-making landscape.
  • 11 Sep 2023 Chang Liu Maynooth
    PACESS: Practical AI-based Cell Extraction and Spatial Statistics for large 3D biological images
    Efficient methodologies to fully extract and analyse large datasets remain the Achilles heels of 3D tissue imaging. Here we present PACESS a pipeline for large-scale data extraction and spatial statistical analysis from 3D biological images. First, using 3D object detection neural networks trained on annotated 2D data, we identify and classify the location of hundreds of thousands of cells contained in large biological images. Then, we introduce a series of statistical techniques tailored to work with spatial data, resulting in a 3D statistical map of the tissue from which multi-cellular interactions can be clearly understood. As illustration of the power of this new approach, we apply this analysis pipeline to an organ known to have a complex and still poorly understood cellular structure: the bone marrow. The analysis reveals coherent, useful biological information on multiple cell population interactions. This novel and powerful spatial analysis pipeline can be broadly used to unravel complex multi-cellular interaction towards unlocking tissue complexity.
  • 18 May 2023 Chris Overton Liverpool
    Modelling the 2022 mpox outbreak
    During the 2022 mpox outbreak, modelling has provided support to policy makers and the incident management team. In this talk, I will give an overview of some of the key modelling work. Firstly, we consider real-time estimation of epidemiological parameters. Such estimation is challenging due to right-truncation and interval-censoring in the real-time data. Through this, we provided the first evidence of pre-symptomatic transmission of mpox. This will be followed by an overview of novel nowcasting models that were developed during the outbreak. With substantial delays between infections occurring and being reported, the epidemic curve suffered from substantial backfilling. Nowcasting methods attempt to account for this backfilling, allowing the epidemic curve to be evaluated in real-time. This is essential for reliable surveillance and timely decision making.
  • 17 May Philip Maini Oxford
    Modelling collective cell movement in development and disease
    Collective movement is ubiquitous in nature, occurring across a vast range of scales, from whales to bacteria. This talk will review some of our work on collective movement at the cell level. It will include (i) a novel partial differential equation (PDE) model derived from consideration of the classical snail-trail model for angiogenesis; (ii) a PDE model that views cancer cell invasion as a co-operative phenomenon; (iii) a hybrid agent-based model for cranial neural crest migration which, coupled with experiments, has led to new biological insights on this phenomenon.
  • 11 May Eva Deinum Wageningen
    Zebrastripes for thirsty plants: the same story twice over?
    The plant cell wall is a versatile material that can meet a wide range of mechanical requirements. The banded patterns in protoxylem form a striking example, enabling these vessels withstand substantial negative pressure and allow for extension at the same time. The required anisotropic material properties largely derive from the location and orientation of the constituting cellulose microfibrils. These, in turn are deposited along the cortical microtubule cytoskeleton. So, using the case of protoxylem as a model system for complex cell wall patterns, the question becomes how cortical microtubules can self-organize into banded patterns. This happens in interaction with another well-known patterning system, the ROP proteins.
    We address this interaction from both sides: how can dynamic microtubules collectively adjust to a predefined ROP pattern and how can an –implicitly microtubule derived– field of diffusion anisotropy orient and change ROP patterns?
    The ROPs can be described as a reaction-diffusion system, which we study using PDEs, complemented with an ODE model of slowly interacting peaks/clusters. The microtubule part of the work extends a long tradition of combined analytical and stochastic simulation approaches, with a close link to experimental quantification. Whereas the simulations are more easily adapted to relevant biological detail, the analytical foundation aids in efficient investigation and interpretation.
    Despite the very different modelling frameworks and proteins involved, our work on ROP proteins provides critical insights into a problem in the stochastic microtubule simulations: there is a deep link between the stable coexistence of multiple clusters of active ROP and maintaining a sufficiently homogeneous distribution of microtubules across the cell cortex.
  • 4 May Samuel Relton Leeds
    Prediction Modelling in the Healthcare System: From Patient to Production
    In this talk we'll go through the full production cycle of building statistical models that are actually used by clinicians within the NHS. Most modelling work takes place using pre-cleaned data and doesn't need to be production-ready, so there are many extra issues to consider when going the extra mile. In particular we'll discuss the modelling for the electronic frailty index+ (eFI+) work which will imminently go live within the SystmOne and EMIS GP systems (totalling over 30M patients). In addition to the usual modelling issues we'll touch on various sources of bias, robust external validation, MHRA registration, and patient/stakeholder engagement that all need to be taken care of to make direct clinical impact on the frontline.

Recent theses

Flavia Feliciangeli
Stochastic compartmental models and CD8+ T cell exhaustion
Sep 2023
Léa Sta
Mathematical models of cell signalling in heterogeneous populations
Mar 2023
Daniel Luque Duque
Network models of T cell receptor repertoires, cross-reactivity, and viral infection
Mar 2023

Bevelynn Williams
Mechanistic intracellular and within-host models of bacterial and viral infections
Feb 2023
Giulia Belluccini
Stochastic models of cell population dynamics and tick-borne virus transmission
Feb 2023
Polly-Anne Jeffrey
Mathematical Modelling of Cellular Receptor-Ligand Dynamics
Oct 2021

Current and forthcoming programs, conferences and workshops


Eco-Evolutionary Dynamics of Fluctuating Populations

Research project   EEDFP

Understanding the origin of species diversity and the evolution of cooperation is a major scientific riddle that resonates with numerous societal concerns, like the rise of antimicrobial resistance or the loss of biodiversity, and is even relevant to epidemiology. Population dynamics traditionally ignores fluctuations and considers static and homogeneous environments. However, fluctuations arising from randomly occurring birth / death events (demographic noise) and the change of environmental conditions (environmental variability), together with the spatial dispersal of species, play a crucial role in understanding how the size and composition of a population jointly evolve in time, i.e. its eco-evolutionary dynamics. Here, we focus on the ubiquitous situation where the eco-evolutionary dynamics of fluctuating populations is shaped by the coupling of demographic noise and environmental variability.

The interdependence of environmental variability and demographic noise is poorly understood but of great importance in microbial communities, which are often subject to sudden and extreme environmental changes. In particular, modelling population of varying size and composition subject to changing external factors is crucial to understand the evolution of microbial antibiotic resistance. In fact, pharmacodynamics largely focuses on the deterministic description of large well-mixed bacterial populations, but fails to account crucial stochastic effects arising in small communities. When antibiotics reduce a large population to a very small one but fail to eradicate it, surviving cells may replicate and restore infections, and these survivors are likely to develop antibiotic resistance. Owing to the small population size, the details of the outcome are subject to large fluctuations.This important example clearly illustrates the need for theoretical advances to shed light on extinction and resistance scenarios in fluctuating environments.

Some recent papers of interest



Secondments at Leeds: Flavia Feliciangeli  Van Thuy Truong

Recent seminars

  • 27 April Rob Noble City-University of London
    Quantifying and explaining modes of evolution
    Characterizing the mode - the way, manner or pattern - of evolution is a central theme in evolutionary biology. In particular, understanding the nature of tumour evolution underpins accurate prognosis and the design of effective treatment strategies. Whereas selective sweeps are prevalent during early tumour growth, later stages exhibit either sparse branching or effectively neutral evolution. I will begin by presenting new insights into the causes and consequences of these different patterns based on mathematical analysis, computational models, and analysis of clinical data. I will show that, within biologically relevant parameter ranges, different spatial structures can generate distinct tumour evolutionary modes. These model predictions are moreover consistent with data for cancer types with corresponding spatial structures. Surprisingly simple mathematical expressions can be derived to explain why selective sweeps are rare except when tumours are relatively very small. Next, to better describe evolutionary modes, I will introduce a new system of rooted-tree indices. Unlike currently popular indices (such as phylogenetic diversity, phylogenetic entropy, Sackin's index and Colless' index), our definitions assign easily interpretable values to all rooted trees, enable meaningful comparison of any pair of trees, and are robust to sampling and measurement errors. Our unified system further enables the plotting of three-dimensional "tree trajectories" that can be used to characterize and compare tree generating processes. Although my work is motivated by questions in cancer research, many of these results are readily applicable to other systems and have potentially wide-ranging applications in evolutionary biology, conservation biology, and elsewhere.
  • 30 March 2023 Otto Sumray (Mathematical Institute, University of Oxford)
    Multiscale rankings of genes in single cell transcriptomics
    Analysis of single-cell transcriptomics often relies on clustering cells and then performing differential gene expression to identify genes that vary between these clusters. These discrete analyses successfully determine cell types and markers, however, continuous variation of gene expression within and between cell types may not be detected. We propose three methods for unsupervised feature selection based on the graph Laplacian that pull out discrete and continuous transcriptional patterns across multiple scales and we apply them to immune and differentiating cell datasets.
  • 9 March 2023
    Felicia Magpantay (Queen's University)
    Challenges in modeling the transmission dynamics of childhood diseases
    Mathematical models of childhood diseases are often fitted using deterministic methods under the assumption of homogeneous contact rates within populations. Such models can provide good agreement with data in the absence of significant changes in population demography or transmission, such as in the case of pre-vaccine era measles. However, accurate modeling and forecasting after the start of mass vaccination has proved more challenging. This is true even in the case of measles which has a well understood natural history and a very effective vaccine. We demonstrate how the dynamics of homogeneous and age-structured models can be similar in the absence of vaccination, but diverge after vaccine roll-out. We also present some fundamental differences in deterministic and stochastic methods to fit models to data, and propose techniques to fit long term time series with imperfect covariate information. The methods we develop can be applied to many types of complex systems beyond those in disease ecology.
  • 24 Feb 2022
    Lea Sta (Leeds)
    Mathematical modelling of a receptor-ligand system MoRN seminar
  • Thu 30 July 2020
    Marc Jenkins (Minnesota)
    CD4+ T cell differentiation during infection
    Abstract: This talk will describe how naive CD4+ T cells differentiate into Th1 or follicular helper T cells during different infections. A two-step model of Th1 differentiation will be described.
  • Audrey Gerard (Oxford)
    CD8 T cell collective behaviour in health and disease
    Wed 11 Dec 2019
    CD8 T cell responses are key to eradicate virus, intracellular bacteria and cancer cells. A crucial feature of this response is to recruit T cells that will kill pathogen-infected cells or tumour cells while sparing healthy tissues. A multitude of CD8 T cell clones are recruited during an immune response, each with distinct T cell antigen receptors (TCR) with different affinity for their antigen. This clonal breadth is consistently observed despite factors favouring dominance of one or a few clones. How and why this diversity exists is unclear. Our central hypothesis is that T cells integrate individual responses into a collective response through direct communication to preserve T cell clonal breadth. We propose that T cells behave collectively in part through direct co-regulation through cytokines, allowing for lower-affinity clones to emerge and survive despite the competitive environment. I will discuss the consequences of direct T cell communication through the cytokine IFNγ on anti-bacterial responses, and how it impedes anti-tumour responses.
  • Oscar Rodriguez de Rivera Ortega (Kent)
    Spatial and spatio-temporal models to understand ecological processes
    Wed 23rd Oct 2019, 12:00-13:00
  • Systems Pharmacology and Pharmacometrics: How Mathematics, Statistics and Data Science Are Impacting Drug Discovery and Development
    Paolo Vicini (Kymab Ltd)
    18 Oct 2019 13.30
    Modern drug discovery and development are rapidly becoming more reliant on rigorously quantitative approaches. In addition to established statistical testing and experimental design techniques, new approaches include pharmacometrics and systems pharmacology. Pharmacometrics is a collection of quantitative tools applied to clinical drug development and trial design, including mixed effect models for drug exposure and response, and covariate selection methods to quantify the impact of demographic, disease status and genetic variation on drug dosing, concentration and effect. Systems pharmacology is an evolution of systems biology, which seeks to harness quantitative, time-dependent pathway models to predict and quantify the effects of pharmacological interventions on downstream biomarkers, ultimately aiding rationalize target and drug candidate selection. This presentation will describe modern drug discovery and development pipelines and the role of pharmacometrics and systems pharmacology, highlighting in particular their interdisciplinary nature and the extent to which they borrow from other discipline, including mathematics, statistics and computer science.
  • Damian Clancy (Heriot-Watt University, UK)
    Approximating persistence time for SIS infections in heterogeneous populations
    Wed 9th Oct 2019, 12:00-13:00
  • Prof. Uwe C Tauber (Department of Physics, Virginia Tech, USA)
    Stochastic Spatial Predator-Prey Models
    Wednesday 2nd Oct 2019, 12:00-13:00
  • A mathematical adventure in immunology Carmen Molina-París
    International Centre for Theoretical Sciences, Bangalore. 7 Jul 2019
  • Thursday 23rd May Dr Maria Nowicka (Department of Pathology and Cell Biology, Columbia University, US)
    Differential impact of self and environmental antigens on the ontogeny and maintenance of CD4+ T cell memory
    Laboratory mice not exposed to overt infections nevertheless develop populations of circulating memory phenotype (MP) CD4+ T cells, presumably in response to environmental, commensal or self-antigens. The relative importance and timing of the forces that generate these populations remain unclear. We combine mathematical models with data from studies tracking the generation of CD4+ MP T cell subsets in mice of different ages, housed in facilities that differ in their `dirtiness'. We infer that both central and effector CD4+ MP T cell populations derive directly from naive CD4 T cells, and are heterogeneous in their rates of turnover. We also infer that early exposure to self and environmental antigens establishes persistent memory populations at levels determined largely, but not exclusively, by the dirtiness of the environment. After the first few weeks of life, however, these populations are continuously supplemented by new memory cells at rates that appear to be independent of environment, likely in response to self or ubiquitous commensal antigens.

Recent visitors

  • Joe Gillard and Tom Laws
  • Mario Castro works on mathematical models of systems where fluctuations are relevant (cellular and receptor immunology) and on pattern formation in spatially extended systems (from tumour cell modelling to cauliflower morphogenesis or nano-structuring). The figure shows comparisons of different mathematical models with real experiments.
  • Madhulika Mishra (IISc Bangalore)
  • Narmada Sambaturu (IISc Bangalore)
  • Sathya Baarathi (IISc Bangalore)
  • Shamik Majumdar (IISc Bangalore)

Recent programs, conferences and workshops

ECMTB 2022   Immunoctoberfest 2022