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

Mohammad A. Safi, Mudassar Imran, Abba Gumel

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

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
Volume131
Issue number1
DOIs
StatePublished - May 2012
Externally publishedYes

Fingerprint

Quarantine
quarantine
Isolation
Basic Reproduction Ratio
periodicity
Model
Nonautonomous Systems
infectious diseases
Globally Asymptotically Stable
Autonomous Systems
Persistence
Periodicity
Nonlinear Differential Equations
Elimination
Exceed
Differential equations
persistence
Fluctuations

Keywords

  • Basic reproduction ratio
  • Isolation
  • Periodicity
  • Quarantine

ASJC Scopus subject areas

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

Cite this

Threshold dynamics of a non-autonomous SEIRS model with quarantine and isolation. / Safi, Mohammad A.; Imran, Mudassar; Gumel, Abba.

In: Theory in Biosciences, Vol. 131, No. 1, 05.2012, p. 19-30.

Research output: Contribution to journalArticle

Safi, Mohammad A. ; Imran, Mudassar ; Gumel, Abba. / Threshold dynamics of a non-autonomous SEIRS model with quarantine and isolation. In: Theory in Biosciences. 2012 ; Vol. 131, No. 1. pp. 19-30.
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