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

Author

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  • Mohammad A. Safi

    (Department of Mathematics, Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan)

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.

Suggested Citation

  • Mohammad A. Safi, 2019. "Global Stability Analysis of Two-Stage Quarantine-Isolation Model with Holling Type II Incidence Function," Mathematics, MDPI, vol. 7(4), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:350-:d:222782
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    Cited by:

    1. Paul, James Nicodemus & Mbalawata, Isambi Sailon & Mirau, Silas Steven & Masandawa, Lemjini, 2023. "Mathematical modeling of vaccination as a control measure of stress to fight COVID-19 infections," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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