Global stability analysis of an SEIR epidemic model with vertical transmission. Issue 3 (2017)

• Record Type: Journal Article
• Authors: Kaddar, Abdelilah; Elkhaiar, Soufiane; Eladnani, Fatiha
• Is Part Of: International journal of dynamical systems and differential equations. Volume 7:Issue 3(2017)
• Page Start: 217
• Page End: 228
• Publication Date: 2017
• Subjects: compound matrix -- generalized incidence function -- geometric approach -- global asymptotic stability -- SEIR epidemic model -- vertical transmission; Differential equations -- Periodicals; 515.35
• Languages: English
• ISSNs: 1752-3583

Abstract

The aim of this paper is to include general incidence function in the SEIR epidemic model with both horizontal and vertical transmission. We focus on the global stability of all possible equilibria: the disease-free equilibrium and the endemic equilibrium. The global stability of the disease-free equilibrium is proved by constructing a suitable Lyapunov function and under some appropriate assumptions on the incidence function, the global dynamics of the endemic equilibrium is determined by the geometric approach.