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An epidemic model for an evolving pathogen with strain-dependent immunity

Griffin, Adam; Roberts, Gareth O.; Spencer, Simon E.F.. 2020 An epidemic model for an evolving pathogen with strain-dependent immunity. Mathematical Biosciences, 330, 108480. 11, pp. https://doi.org/10.1016/j.mbs.2020.108480

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Abstract/Summary

Between pandemics, the influenza virus exhibits periods of incremental evolution via a process known as antigenic drift. This process gives rise to a sequence of strains of the pathogen that are continuously replaced by newer strains, preventing a build up of immunity in the host population. In this paper, a parsimonious epidemic model is defined that attempts to capture the dynamics of evolving strains within a host population. The ‘evolving strains’ epidemic model has many properties that lie in-between the Susceptible–Infected–Susceptible and the Susceptible–Infected–Removed epidemic models, due to the fact that individuals can only be infected by each strain once, but remain susceptible to reinfection by newly emerged strains. Coupling results are used to identify key properties, such as the time to extinction. A range of reproduction numbers are explored to characterise the model, including a novel quasi-stationary reproduction number that can be used to describe the re-emergence of the pathogen into a population with ‘average’ levels of strain immunity, analogous to the beginning of the winter peak in influenza. Finally the quasi-stationary distribution of the evolving strains model is explored via simulation.

Item Type: Publication - Article
Digital Object Identifier (DOI): https://doi.org/10.1016/j.mbs.2020.108480
UKCEH and CEH Sections/Science Areas: Hydro-climate Risks (Science Area 2017-)
ISSN: 0025-5564
Additional Information. Not used in RCUK Gateway to Research.: Open Access paper - full text available via Official URL link.
Additional Keywords: epidemiology, probabilistic models, quasistationary distributions
NORA Subject Terms: Health
Biology and Microbiology
Date made live: 28 Oct 2020 12:09 +0 (UTC)
URI: http://nora.nerc.ac.uk/id/eprint/528798

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