Local asymptotic stability of an SIS epidemic model with variable population size and a delay

Abstract

We study a SIS epidemic model with an exponential demographic structure and a delay corresponding to the infectious period. The disease spread is described by a delay differential equation. Equilibriums and the basic reproduction number θ are identified. Using the monotone dynamical systems theory, local asymptotic stability of the two steady states is completely determined. Numerical simulations are carried out to illustrate the theoretical 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).…”