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

First Online: 06 January 2012 Received: 15 August 2011 Accepted: 13 December 2011 DOI :
10.1007/s12064-011-0148-6

Cite this article as: Safi, M.A., Imran, M. & Gumel, A.B. Theory Biosci. (2012) 131: 19. doi:10.1007/s12064-011-0148-6
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.

Keywords Quarantine Isolation Periodicity Basic reproduction ratio

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Authors and Affiliations 1. Department of Mathematics The Hashemite University Zarqa Jordan 2. Department of Mathematics University of Manitoba Winnipeg Canada