Global asymptotic stability of SIRI diseases models using monotone dynamical systems theory

Abstract

In this paper, we consider the global asymptotic stability of the free and the endemic equilibrium of an SIRI epidemiological model with demographic structure. We show that the system is cooperative and irreducible on the closure of an open order convex subset Σ of the space R 3. Moreover, we prove that the compactness condition (T) always holds, and consequently the free and the endemic equilibrium are globally asymptotically stable on Σ. At the end of this work, numerical simulations are presented to illustrate analytical results.

Cooperative system analysis of the Ebola virus epidemic model

“…The work of Smith and his collaborators (Smith & Thieme, 1990, 1991; Hirsch & Smith, 2005; Smith, 2008) improved the results of the Hirsch and used the theory of cooperative and irreducible systems in different types of ODEs with applications to biological systems. The application of the theory of cooperative systems in the epidemiological model is given in (Iggidr, Niri, & Moulay Ely, 2010), more recent works in (Niri, Kabli, & El moujaddid, 2015), and an epidemiological model with delay in (El Karkri & Niri, 2014; Niri & El Karkri, 2015).…”