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Open PhD Project Positions


Select on the project for further information.

To learn about other projects that students are doing as part of the MathSys CDT, please see the MathSys II CDT Student profiles.

Project Title: Computational modelling of neurotransmitter release and synaptic microcircuits in health and disease

Internal Supervisor: Yulia Timofeeva (Computer Science)
External Partner: Prof Kirill Volynski group, University College London

Project Description

Synaptic release of neurotransmitters provides the basis for communication among neurons in the brain. When an action potential invades a presynaptic terminal, it triggers fast fusion of synaptic vesicles filled with neurotransmitters. Neurotransmitters quickly diffuse towards the postsynaptic neuron, where they bind to specific receptors and evoke further electrical and/or chemical signalling. Although the general molecular mechanisms of transmitter release and postsynaptic activation are well established, the precise regulation of synaptic plasticity at different synapses remains incompletely resolved. The main difficulty studying this regulation at the level of individual synapses is that the majority of presynaptic terminals and postsynaptic target zones in the brain are very small, and as a result the experimental techniques are confronted with serious limitations. Our previous modelling efforts have been exclusively focused on the presynaptic component (e.g., Ermolyuk et al., Nature Neuroscience, 2013; Timofeeva and Volynski, Frontiers in Cellular Neuroscience, 2015; Chamberland et al, PNAS, 2018; Mendonca et al, Nature Communications, 2022; Norman et al, Communications Biology, 2023).
The primary goal of this project is to advance computational modelling by creating novel experimentally constrained reaction-diffusion models that encompass both presynaptic and postsynaptic elements of small synaptic circuits. These realistic models will be integrated with experimental methods to explore synaptic modulation and plasticity across various synaptic architectures in both healthy cells and those affected by mutations associated with neurological disorders. The project will involve close collaboration with Prof Kirill Volynski group in University College London, and it will give an opportunity to take advantage of direct interaction with the experimental scientists.
The project will require good modelling skills and an interest in applying theoretical approaches to understanding biological data. Implementation can be performed using any programming language (for anyone with strong programming skills), or alternatively it can be done in Virtual Cell (, a comprehensive platform for modelling cell biological systems).

Project Title: Parameter estimation and model selection for crowd dynamics

Supervisor:: Dr Susana Gomes (Mathematics Institute)

Project Description

Understanding the behaviour of crowds is crucial for safety and transport management: on the one hand, it allows to make predictions of people’s behaviour (e.g., what their reaction would be in an evacuation), and on the other hand it facilitates better design of rooms, buildings or even streets to optimise movement. There are many types of models for pedestrian dynamics, ranging from microscopic models (agent-based models that describe the trajectory of individual pedestrians) to kinetic models to macroscopic ones (a PDE model describing the density of a crowd). Most models in the literature rely on the fundamental diagram: a tool that engineers use to characterise the speed of pedestrians to the average density they experience. Although there is a general agreement on the shape of this function, its parametrisation depends strongly on the measurement and averaging techniques used as well as the experimental setup considered. The goal of this project is to improve our understanding of this function, and to quantify how well different models (involving different functional forms of the fundamental diagram) describe real-life behaviour. The project will focus on connection between macroscopic models for trajectories and PDE models for the density of the crowd and the student will have freedom to choose between several inference techniques (from Bayesian estimation to reinforcement learning), based on data available from external partners.

Project Title: Multi-scale mathematical modelling: at the interface between analysis and scientific computing

Supervisor: Dr Radu Cimpeanu (Mathematics Institute)

Project Description

I am interested in supervising projects at the intersection between mathematical modelling, asymptotic analysis, solutions for ordinary/partial differential equations and high performance computing (including computational linear algebra and large scale system solvers).

Most of my active research streams include topics in fluid mechanics such as interfacial flows (modelling, analysis, simulation and applications of drops, bubbles and liquid films), rheological flows (from chocolate to de-icing fluids) and novel mathematical models for the alternative protein industry.

Multi-physics effects involving acoustics, heat transfer or electromagnetism are also often included in the modelling activity of my research group. From a mathematical standpoint, there are exciting opportunities to combine classical (continuum) modelling with discrete and data scientific streams, as well as integrating approaches such as control theory, hybrid modelling or data-driven equation discovery into areas previously unexplored with such tools.

More generally, work on any of the above will likely involve a mixture of analytical and computational techniques (which can be tailored depending on your own interests and what skillset you wish to develop), as well as the interplay between them.

I am always happy to co-create projects, and encourage you to consult the supervision section of my webpage for a glimpse at past and current activities, as well as ideas for future project streams.

Project Title: Epidemiology: Quantifying the impact of highly pathogenic avian influenza in the UK wild bird population.

Supervisors: Ed Hill Link opens in a new window(Maths), Erin GorsichLink opens in a new windowLink opens in a new window (Life Sciences), Mike TildesleyLink opens in a new windowLink opens in a new window (Maths & Life Sciences) and Matt KeelingLink opens in a new windowLink opens in a new window (Maths & Life Sciences)

Project Description

Highly Pathogenic Avian Influenza (HPAI) has long been associated with substantial outbreaks and losses in poultry farms, with occasional spill-over into human populations – although, fortunately there is limited evidence of transmission between humans. Wild waterfowl are well documented reservoirs, and since 2022 there has been an unprecedented decline in many wild bird populations driven by HPAI (seabird colonies most affected). Quantifying the spread and impact of HPAI is a necessary first step in the conservation of the UK wild bird populations. Fortunately, the UK has extensive population records collected by professional and amateur ornithologists that can aid such efforts. This project will collate the available data to investigate the potential impact of HPAI in wild bird populations since 2022, develop projections and model the prospective impacts of conservation practices intended to mitigate HPAI infection risk.

Required skills: strong quantitative training, programming skills advised.

Project Title: Epidemiology: Modelling the spread and control of highly pathogenic avian influenza in poultry and quantifying zoonotic transmission risk.

Supervisors: Mike TildesleyLink opens in a new window (Maths & Life Sciences) and Ed Hill Link opens in a new windowLink opens in a new windowLink opens in a new windoLink opens in a new window(Mathematics Institute)

Project Description

In recent years, cases of Highly Pathogenic Avian Influenza (HPAI) H5N1 in poultry have been increasing worldwide and this, combined with the recently reported cases of H5N1 in mammalian species and sporadically reported human cases, has raised concerns regarding the potential for sustained zoonotic transmission to occur over the coming years. This project will build upon previous work that has been carried out on modelling the spread of HPAI H5N1 in South and South East Asia, as well as recent work in the UK, to establish the ongoing risk of HPAI to domestic poultry farms both in the UK and in other countries and the potential for zoonotic transmission to occur. The project will be carried out in collaboration with the Animal and Plant Health Agency (APHA) as well as relevant international veterinary agencies to provide timely advice to minimise the future impact of HPAI.

Required skills: strong quantitative training.

Project Title: Epidemiology: Controlling measles outbreaks in the UK

Supervisors: Matt Keeling (Mathematics Institute & School of Life Sciences) and Ed Hill Link opens in a new windoLink opens in a new window(Mathematics Institute)
External partner: Department of Health & Social Care

Project Description

Measles was a common disease and caused substantial loss of life before the roll-out of vaccination in the 1970s. In recent years, the uptake of measles (MMR) vaccine in many areas has fallen sharply, leading to fears that there is a build-up of susceptibility in the population; although this may be partially counter by reduced community mixing compared to pre-vaccination. Consequently, there are concerns of intense localised outbreaks occurring soon, but also considerable uncertainty.

This project has two primary modelling aims. The first is to use an age-structured infectious disease model to investigate the potential for future localised outbreaks. The second is to use health economics to evaluate the cost-effectiveness of the current vaccination programme.
Data available to help study this problem includes: historical uptake of MMR vaccine [1], notification of suspected measles cases [2].

The initial months of the project would provide the student with a foundation in infectious disease modelling and health economic modelling. The student will also begin developing skills in communicating research to policy makers. The project could then be further developed, in collaboration with the Department of Health and Social Care (DHSC) into topics including

  • Developing a meta-population model to investigate reintroduction dynamics
  • Studying the implications of systemic loss of immunity following measles infection.
  • Parameter inference methodology comparisons (MCMC vs ABC)


Project Title: Modelling of the epidemiological and demographic drivers of canine rabies transmission

Supervisor: Mike Tildesley (Mathematics Institute & School of Life Sciences)
External Partner: Kristyna Rysava (Centres for Disease Control and Prevention, Atlanta, USA)

Disease systems are complex in that they typically involve multiple drivers demonstrating different patterns of interaction across multiple scales, of which many remain poorly understood. The most effective disease control strategies should be deployed accordingly to the local epidemiological dynamics. Uncertainty, however, hinders decision-making given substantial heterogeneity in key epidemiological and ecological parameters of a disease and its vector population across spatial and temporal scales.

Canine rabies offers a unique study system to examine the extent to which finer-resolution heterogeneity in transmission and control shape disease dynamics observed at the population level. In most rabies-affected settings, local elimination is actively attempted with only limited or short-term results being commonplace. Although the observed long-term persistence of canine rabies at remarkably low incidence remains an enigma, likely drivers are associated with generally high spatial connectivity and variability in the force and re-emergence of infection between settings, resulting from inconsistent control efforts and high demographic turnover. Most existing models of rabies transmission either simplify the role of stochasticity and heterogeneity or can only simulate dynamics at a small spatial scale, providing spatially explicit results that are ungeneralizable across settings. Consequently, there is a pressing need for realistic models that are built on an epidemiological and ecological backbone yet universal enough to offer straightforward guidance to evaluate and ensure progress towards elimination targets.

Using spatially and temporally detailed data on rabies incidence and vaccination collected over the last 10 years in Bali, Indonesia, the student will develop a series of progressively more complex rabies transmission models fitted to the partially observed case data to the epidemiological and demographic drivers of the disease dynamics, leading to more accurate predictions of rabies spread and insights into the principles of effective interventions. The resultant framework can be utilised to answer a set of theoretical and applied questions that will improve our understanding of rabies transmission and the impact of existing interventions in the local system. Such results are anticipated to provide applicable guidelines for decision making in the context of vaccination planning and rabies surveillance.

Project Title: Models of Bacterial Chemotaxis with Flow

Supervisors: Matthew Turner (Physics)

It has been known for many years that Bacteria are able to direct their motion up concentration gradients of nutrient molecules [1]. This process is known as Chemotaxis and it bestows a fitness advantage over other bacteria, that cannot move in this way. Simple models of Chemotaxis involve the bacteria swimming in (nearly) a straight trajectory, known as a “run”, before reversing the rotation of tail-like flagellae to generate a random re-orientation, known as a “tumble”. If the bacteria sense the nutrients becoming more/less concentrated as they move then they tend to have longer/shorter runs, respectively. Such strategies can successfully navigate up concentration gradients. The motion can be described using, e.g. Langevin or Fokker-Planck equations. Nonetheless, these strategies are usually studied in the absence of flows. However, the bacteria themselves must set up a flow field in order to move, so the effect of neglecting the effect of flow on nutrient transport is unclear. This project will involve an investigation of the effect of such flows that move the nutrients around.

You will begin the PhD by reviewing literature models of bacterial chemotaxis [1,2] and then analysing a mathematical description of these models in the absence of fluid flows. Early objectives would be to complete this analysis and to have started to study the “squirmer” model for the fluid flow around a single micro-swimmer [3,4].

Later goals for the project would be to combine a mean-field description of the fluid flow with the chemotactic response. Do steady-state bacterial distributions exist and are they stable? Alternatively, only dynamical solutions may arise. Various choices for the nutrient injection process and additional background fluid flows can also be studied. Two questions to address would be (i) Do steady exist in which there is non-zero average fluid flow and
are they stable? (ii) Does the dynamics depend on the nutrient injection process, the dimensionality of the problem or the density or activity of bacteria? This project can be taken in a number of other directions, e.g. to include reproduction and death. Finally, it would be interesting to undertake an analysis of more complex chemotactic strategies.

Ideally the student would have some experience in fluid dynamics, dynamical systems, PDEs and analysis.

[1] Berg, H.C., Random Walks in Biology, Princeton University Press (1993).
[2] Keller, E. F. and Segel, L. A., J. Theo. Biol. 30, 225-234 (1971).
[3] Lighthill, M. J., Comms. Pure and Appl. Math. 5, 109–118 (1952).
[4] Blake, J. R., Journal of Fluid Mechanics. 46, 199–208 (1971)