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

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

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Official URL: https://doi.org/10.1016/j.mbs.2020.108480

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Abstract

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: Journal Article
Subjects: R Medicine > RA Public aspects of medicine
Divisions: Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Epidemiology, Epidemiology -- Mathematical models, Epidemiology -- Statistical methods, Case-control method
Journal or Publication Title: Mathematical Biosciences
Publisher: Elsevier Science Inc.
ISSN: 0025-5564
Official Date: December 2020
Dates:
DateEvent
December 2020Published
28 September 2020Available
21 September 2020Accepted
Volume: 330
Article Number: 108480
DOI: 10.1016/j.mbs.2020.108480
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
HO23364/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/R018561/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
MR/P026400/1[MRC] Medical Research Councilhttp://dx.doi.org/10.13039/501100000265
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