Mathematical Biology and Medicine


Current and forthcoming programs, conferences and workshops


9 March, 12:00-13:00
MALL, School of Mathematics Felicia Magpantay (Queen's University)
Challenges in modeling the transmission dynamics of childhood diseases
Abstract: 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.

Recent theses

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

Some recent papers of interest


Eco-Evolutionary Dynamics of Fluctuating Populations

Research project


Secondments at Leeds: Flavia Feliciangeli  Van Thuy Truong

Recent seminars

  • 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