Threshold dynamics of a non-autonomous SEIRS model with quarantine and isolation

Mohammad A. Safi, Mudassar Imran, Abba B. Gumel

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


A model for assessing the effect of periodic fluctuations on the transmission dynamics of a communicable disease, subject to quarantine (of asymptomatic cases) and isolation (of individuals with clinical symptoms of the disease), is considered. The model, which is of a form of a non-autonomous system of non-linear differential equations, is analysed qualitatively and numerically. It is shown that the disease-free solution is globally- asymptotically stable whenever the associated basic reproduction ratio of the model is less than unity, and the disease persists in the population when the reproduction ratio exceeds unity. This study shows that adding periodicity to the autonomous quarantine/isolation model developed in Safi and Gumel (Discret Contin Dyn Syst Ser B 14:209-231, 2010) does not alter the threshold dynamics of the autonomous system with respect to the elimination or persistence of the disease in the population.

Original languageEnglish (US)
Pages (from-to)19-30
Number of pages12
JournalTheory in Biosciences
Issue number1
StatePublished - May 1 2012
Externally publishedYes


  • Basic reproduction ratio
  • Isolation
  • Periodicity
  • Quarantine

ASJC Scopus subject areas

  • Statistics and Probability
  • Ecology, Evolution, Behavior and Systematics
  • Applied Mathematics


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