Global stability analysis of an SEIR epidemic model with vertical transmission. Issue 3 (2017) - Kaddar, Abdelilah; Elkhaiar, Soufiane; Eladnani, Fatiha
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.