Elsevier

Mathematical Biosciences

Volume 330, December 2020, 108480
Mathematical Biosciences

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

https://doi.org/10.1016/j.mbs.2020.108480Get rights and content
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open access

Highlights

  • A novel model for a pathogen evolving via mutations to escape host immunity.

  • An equivalence relation fixes the model against the most recently emerged strain.

  • Average behaviour is analysed through the quasi-stationary distribution.

  • Coupling to existing models yields limits on the distribution of the time to extinction.

  • A reproduction number captures re-emergence into a population with average immunity.

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.

MSC

92D30
97M60
60J28

Keywords

Epidemiology
Probabilistic models
Quasistationary distributions

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