Sustained oscillations in an evolutionary epidemiological model of influenza A drift

Pierre Magal, Shigui Ruan

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

Understanding the seasonal/periodic reoccurrence of influenza will be very helpful in designing successful vaccine programmes and introducing public-health interventions. However, the reasons for seasonal/periodic influenza epidemics are still not clear, even though various explanations have been proposed. In this paper, we study an agestructured type evolutionary epidemiological model of influenza A drift, in which the susceptible class is continually replenished because the pathogen changes genetically and immunologically from one epidemic to the next, causing previously immune hosts to become susceptible. Applying our recently established centre manifold theory for semilinear equations with non-dense domain, we show that Hopf bifurcation occurs in the model. This demonstrates that the age-structured type evolutionary epidemiological model of influenza A drift has an intrinsic tendency to oscillate owing to the evolutionary and/or immunological changes of the influenza viruses.

Original languageEnglish (US)
Pages (from-to)965-992
Number of pages28
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume466
Issue number2116
DOIs
StatePublished - Apr 8 2010

Keywords

  • Endemic equilibrium
  • Epidemic model
  • Hopf bifurcation
  • Influenza A drift
  • Stability

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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