Authors: J. El Karkri; K. Niri
Addresses: Laboratory MACS, Department of Mathematics and Computer Science, Faculty of sciences Ain Chock (FSAC), Hassan II University of Casablanca, Km 8 Route d'El Jadida, B.P 5366 Maarif Casablanca 20100, Morocco ' Laboratory MACS, Department of Mathematics and Computer Science, Faculty of sciences Ain Chock (FSAC), Hassan II University of Casablanca, Km 8 Route d'El Jadida, B.P 5366 Maarif Casablanca 20100, Morocco
Abstract: In this paper, we investigate global stability of the endemic steady state of the SIS epidemic model studied recently in terms of fluctuations. The epidemiological model has an exponential demographic structure, disease-related deaths and a delay corresponding to the infectious period. The disease spread is governed by a scalar delay differential equation. Our study is mainly based on the monotone dynamical systems theory. We begin by simplifying the classical framework of stability analysis for non-quasi-monotone scalar autonomous delay differential equations by using recent results on essentially strongly order-preserving semiflows. Under certain conditions, it is proved that the endemic equilibrium is globally asymptotically stable on a closed subset of the phase space C. To our knowledge, this is the first study proving the endemic steady state's global stability for this model. Numerical simulations which illustrate the results are carried out.
Keywords: essentially strongly order-preserving semiflow; exponential ordering; global asymptotic stability; non-quasi-monotone delay differential equations; epidemics; stability analysis; modelling; fluctuations; SIS epidemiological model; monotone dynamical systems theory; numerical simulation.
International Journal of Dynamical Systems and Differential Equations, 2016 Vol.6 No.2, pp.173 - 185
Received: 13 Aug 2015
Accepted: 12 Dec 2015
Published online: 25 Jun 2016 *