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Mathematics 2019, 7(4), 350; https://doi.org/10.3390/math7040350

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
Received: 28 February 2019 / Revised: 27 March 2019 / Accepted: 10 April 2019 / Published: 15 April 2019
(This article belongs to the Section Mathematics and Computers Science)
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Abstract

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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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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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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