Mathematical Analysis of an SIQR Influenza Model with Imperfect Quarantine

Mustafa Erdem, Muntaser Safan, Carlos Castillo-Chavez

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The identification of mechanisms responsible for recurrent epidemic outbreaks, such as age structure, cross-immunity and variable delays in the infective classes, has challenged and fascinated epidemiologists and mathematicians alike. This paper addresses, motivated by mathematical work on influenza models, the impact of imperfect quarantine on the dynamics of SIR-type models. A susceptible-infectious-quarantine-recovered (SIQR) model is formulated with quarantined individuals altering the transmission dynamics process through their possibly reduced ability to generate secondary cases of infection. Mathematical and numerical analyses of the model of the equilibria and their stability have been carried out. Uniform persistence of the model has been established. Numerical simulations show that the model supports Hopf bifurcation as a function of the values of the quarantine effectiveness and other parameters. The upshot of this work is somewhat surprising since it is shown that SIQR model oscillatory behavior, as shown by multiple researchers, is in fact not robust to perturbations in the quarantine regime.

Original languageEnglish (US)
Pages (from-to)1-25
Number of pages25
JournalBulletin of Mathematical Biology
DOIs
StateAccepted/In press - Jun 12 2017

Fingerprint

Quarantine
mathematical analysis
quarantine
influenza
Influenza
Mathematical Analysis
Imperfect
Human Influenza
Model
cross immunity
Uniform Persistence
Coinfection
Age Structure
Variable Delay
Disease Outbreaks
SIR
Immunity
Hopf bifurcation
Alike
Dynamic Process

Keywords

  • Equilibria
  • Hopf bifurcation
  • Imperfect quarantine
  • SIQR model
  • Stability analysis
  • Uniform persistence

ASJC Scopus subject areas

  • Neuroscience(all)
  • Immunology
  • Mathematics(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Pharmacology
  • Environmental Science(all)
  • Agricultural and Biological Sciences(all)
  • Computational Theory and Mathematics

Cite this

Mathematical Analysis of an SIQR Influenza Model with Imperfect Quarantine. / Erdem, Mustafa; Safan, Muntaser; Castillo-Chavez, Carlos.

In: Bulletin of Mathematical Biology, 12.06.2017, p. 1-25.

Research output: Contribution to journalArticle

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