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Joe Hilton

I began my PhD in October 2015, supervised by Matt Keeling (Maths, Life Sciences, Zeeman Institute) and Ian Hall (University of Manchester). My research focused on stochastic models for both novel and endemic infections in structured populations. I have now completed my PhD and am a research fellow based in SBIDER (Systems Biology and Infectious Disease Epidemiology Research), attached to the GeMVi project. The information on this page was accurate at the time of my thesis submission in autumn 2019.

Where to find me:

Room 5.25, Mathematical Sciences Building


PhD Project(s)

My PhD follows two main threads:

  • Endemic diseases in structured populations. The use of age- and household-structured models for childhood diseases such as measles and mumps is well established. However, these infections tend to circulate over long timescales, during which the underlying contact structures can change dramatically, with children growing into adults and moving between different households. My work in this area focuses on developing structured infection models with dynamic population structure, informed by real-world data from statistical agencies and contact surveys.
  • Behaviour of early outbreaks. The early behaviour of an epidemic is well-approximated by a relatively simple class of stochastic model known as a branching process, which focus on the spreading behaviour of early cases. During my PhD I have considered the effect of household structure on this spreading behaviour and how well different probability distributions can account for the distribution of cases generated.

Research internship: Modelling Infection, Household and Demographic Change

I worked with my PhD supervisor Matt Keeling on a three month research internship (October-December 2016) supported by the EPSRC Global Challenges Research Fund. Our focus was on developing a model for the spread of an endemic disease which included accounts for both age and household structure. This project formed the basis of the "Endemic diseases" section of my PhD.


  • Hilton Joe and Keeling Matt J. Incorporating household structure and demography into models of endemic disease. 16. J. R. Soc. Interface

Conference Contributions:

  • Talk: A household-structured approach to endemic infections. Workshop on Stochastic Modelling in Health and Disease, Leeds, UK, Sept 2019.
  • Talk: Endemic diseases with household structure and demography. 10th Swedish Meeting on Mathematics in Biology, Stockholm, Sweden, Dec 2018
  • Poster: Modelling endemic infections with households and demography. IDDconf, Ambleside, UK, Sept 2018
  • Talk: Household models for endemic diseases. European Conference of Mathematical and Theoretical Biology, Lisbon, Portugal, Aug 2018
  • Talk: Extending household models to endemic settings. Epidemics 6, Sitges, Spain, Dec 2017
  • Poster: Extending household models to endemic settings. Mathematical Challenges From The Life Sciences, Warwick, UK, Sept 2017
  • Talk: Extending household models to endemic settings. Conference on Infectious Disease Dynamics, Ambleside, UK, Sept 2017
  • Talk: Modelling near-critical diseases with branching processes. University of Melbourne-University of Manchester joint research workshop: New approaches to infectious disease modelling for epidemiological understanding and public health impact, Manchester, UK, July 2017
  • Poster: Modelling emerging diseases using branching processes. Conference: Developing efficient methodologies for modelling stochastic dynamical systems in biology, Bath, UK, April 2017
  • Poster: Modelling emerging diseases using branching processes. Public Health England Research and Applied Epidemiology Conference, Warwick, UK, March 2017

Grants and Awards

IMA Small Grant Scheme, awarded December 2018 by the Institute of Mathematics and its Applications in order to fund my attendance at the 10th Swedish Meeting on Mathematics in Biology.

Background and Previous Projects

Before joining the MathSys CDT, I completed my MMath at Warwick, graduating with first class honours in 2014. I graduated from the MathSys MSc in January 2016. My research experience during this time includes the following projects:

  • Branching Process Models for Weakly Transmissible Diseases, supervised by Matt Keeling and Ian Hall
  • Critical Community Size and Extinctions for Livestock Disease, supervised by Matt Keeling and Simon Gubbins (Pirbright)
  • Levins Metapopulation Dynamics for Stochastic Populations, supervised by Matt Keeling
  • Behavioural Epidemics with a Complex Stifling Contagion, supervised by Thomas House (then Warwick, now at Manchester) and Daniel Sprague (then Warwick, now at Spectra Analytics)

Other activities


I was seminar tutor for the module "Population Dynamics: Ecology & Epidemiology" in the 2016-17 and 2017-2018 academic years.

Warwick SIAM Chapter

From 2015-2017 I was on the exec committee of Warwick's student chapter of SIAM, the Society for Industrial and Applied Mathematics. Our focus is on engaging students and stimulating discussions focused on applied and computational mathematics. We host regular talks featuring speakers from industry, as well as mini-conferences which bring together the worlds of industry and academia and give students a platform to present their research. All members of our student chapter are eligible for a free SIAM membership, giving them access to journals, newsletters and online resources.