This paper aims to study the global stability of an Ebola virus epidemic model. Although this epidemic ended in September 2015, it devastated several West African countries and mobilized the international community. With the recent cases of Ebola in the Democratic Republic of the Congo (DRC), the threat of the reappearance of this fatal disease remains. Therefore, we are obligated to be prepared for a possible re-emerging of the disease. In this work, we investigate the global stability analysis via the theory of cooperative systems, and we determine the conditions that lead to global stability diseases free and endemic equilibrium.

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.