Stability analysis of a delayed SIS epidemiological model

Stability Analysis of a Delayed Immune Response Model to Viral Infection

“…(2.3) is said to satisfy the Assumption (TD1) on Ω if h maps bounded subsets of Ω to bounded subsets of ℝ , and the positive semi-orbit of every solution of (2.3) with ∈ Ω is bounded. See for instance [5,40]. For 𝜇 > 0 , consider the set As pointed out in [27,30], C is a closed cone in the Banach space C with empty interior.…”

“…We write 𝜙 < 𝜇 𝜓 if ≤ and ≠ . The reader is referred to [5,27,30] for further details on the partial order ≤ .…”

“…Later, Yi and collaborators introduced the concept of essentially strongly order-preserving semi-flows and provided a simplified compactness assumption [39,40]. Recently, and using the results of [40], Niri and El Karkri have established a simplified framework for stability analysis of equilibriums for nonquasimonotone autonomous scalar delay differential equations [5,6]. The obtained theorems have been applied in the same articles to an SIS compartmental epidemiological model with infection period, variable population size and deaths caused by infection [5,6].…”

“…In the present paper, the method is mainly based on the framework developed in [5,6]. We aim to establish sufficient conditions of local and global asymptotic stability for the equilibria of the Eq.…”

“…The next section provides some preliminary results concerning existence, regularity and smoothness of solutions of autonomous scalar delay differential equations as well as a reminder of some important results of monotone dynamical systems theory for non-quasimonotone scalar delay differential equations. Most of the results and definitions in this section are taken from [5,6,8,27,30,40]. In Sect.…”