Compositional modelling of immune response and virus transmission dynamics

W. Waites, M. Cavaliere, V. Danos, R. Datta, R. M. Eggo, T. B. Hallett, D. Manheim, J. Panovska-Griffiths, T. W. Russell, V. I. Zarnitsyna

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
25 Downloads (Pure)


Transmission models for infectious diseases are typically formulated in terms of dynamics between individuals or groups with processes such as disease progression or recovery for each individual captured phenomenologically, without reference to underlying biological processes. Furthermore, the construction of these models is often monolithic: they do not allow one to readily modify the processes involved or include the new ones, or to combine models at different scales. We show how to construct a simple model of immune response to a respiratory virus and a model of transmission using an easily modifiable set of rules allowing further refining and merging the two models together. The immune response model reproduces the expected response curve of PCR testing for COVID-19 and implies a long-tailed distribution of infectiousness reflective of individual heterogeneity. This immune response model, when combined with a transmission model, reproduces the previously reported shift in the population distribution of viral loads along an epidemic trajectory. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Original languageEnglish
Article number20210307
Pages (from-to)1-24
Number of pages24
JournalPhilosophical Transactions A: Mathematical, Physical and Engineering Sciences
Issue number2233
Early online date15 Aug 2022
Publication statusPublished - 3 Oct 2022


  • immune response model
  • transmission models
  • compositional modelling
  • immune response
  • virus transmission dynamics


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