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Global Stability Analysis of Two-Stage Quarantine-Isolation Model with Holling Type II Incidence Function

Department of Mathematics, Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan
Mathematics 2019, 7(4), 350; https://doi.org/10.3390/math7040350
Received: 28 February 2019 / Revised: 27 March 2019 / Accepted: 10 April 2019 / Published: 15 April 2019
(This article belongs to the Section Mathematics and Computer Science)
A new two-stage model for assessing the effect of basic control measures, quarantine and isolation, on a general disease transmission dynamic in a population is designed and rigorously analyzed. The model uses the Holling II incidence function for the infection rate. First, the basic reproduction number ( R 0 ) is determined. The model has both locally and globally asymptotically stable disease-free equilibrium whenever R 0 < 1 . If R 0 > 1 , then the disease is shown to be uniformly persistent. The model has a unique endemic equilibrium when R 0 > 1 . A nonlinear Lyapunov function is used in conjunction with LaSalle Invariance Principle to show that the endemic equilibrium is globally asymptotically stable for a special case. View Full-Text
Keywords: quarantine; isolation; stability; uniformly persistent; Holling type II quarantine; isolation; stability; uniformly persistent; Holling type II
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Safi, M.A. Global Stability Analysis of Two-Stage Quarantine-Isolation Model with Holling Type II Incidence Function. Mathematics 2019, 7, 350.

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