Title: Global asymptotic stability of an SIS epidemic model with variable population size and a delay

Authors: Jaafar El Karkri; Khadija Niri

Addresses: Department of Mathematics and Computer Science, Laboratory MACS, Faculty of Sciences Ain Choq, Hassan II University, Km 8 Route d'El Jadida, B.P 5366 Maarif, Casablanca 20100, Morocco ' Department of Mathematics and Computer Science, Laboratory MACS, Faculty of Sciences Ain Choq, Hassan II University, Km 8 Route d'El Jadida, B.P 5366 Maarif, Casablanca 20100, Morocco

Abstract: An SIS epidemiological model with an exponential demographic structure and a delay corresponding to the infectious period is studied. We derive sufficient conditions for the global asymptotic stability of the infected steady state. The study is mainly based on very recent results of the monotone dynamical systems theory rarely used in mathematical epidemiology. We propose an improved and practical version of an important result in the theory. The obtained results are a partial - but important - resolution of the open problem proposed by Hethcote and van den Driessche in 1995. Numerical simulations are conducted to demonstrate our theoretical results.

Keywords: delay differential equation; essentially strongly order-preserving semi-flows; global asymptotic stability; monotone dynamical systems; SIS epidemic model.

DOI: 10.1504/IJDSDE.2017.10008428

International Journal of Dynamical Systems and Differential Equations, 2017 Vol.7 No.4, pp.289 - 300

Available online: 09 Oct 2017 *

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