Global asymptotic dynamics of a model for quarantine and isolation

Mohammad A. Safi, Abba B. Gumel

Research output: Contribution to journalArticle

23 Scopus citations

Abstract

The paper presents an SEIQHRS model for evaluating the combined impact of quarantine (of asymptomatic cases) and isolation (of individuals with clinical symptoms) on the spread of a communicable disease. Rigorous analysis of the model, which takes the form of a deterministic system of nonlinear differential equations with standard incidence, reveal that it has a globally-asymptotically stable disease-free equilibrium whenever its associated reproduction number is less than unity. Further, the model has a unique endemic equilibrium when the threshold quantity exceeds unity. Using a Krasnoselskii sub-linearity trick, it is shown that the unique endemic equilibrium is locally-asymptotically stable for a special case. A nonlinear Lyapunov function of Volterra type is used, in conjunction with LaSalle Invariance Principle, to show that the endemic equilibrium is globally-asymptotically stable for a special case. Numerical simulations, using a reasonable set of parameter values (consistent with the SARS outbreaks of 2003), show that the level of transmission by individuals isolated in hospitals play an important role in determining the impact of the two control measures (the use of quarantine and isolation could offer a detrimental population-level impact if isolation-related transmission is high enough).

Original languageEnglish (US)
Pages (from-to)209-231
Number of pages23
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume14
Issue number1
DOIs
StatePublished - Jul 1 2010
Externally publishedYes

Keywords

  • Equilibria
  • Isolation
  • Quarantine
  • Reproduction number
  • Stability

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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