Authors: Abdelilah Kaddar; Soufiane Elkhaiar; Fatiha Eladnani
Addresses: Faculté des Sciences Juridiques, Economiques et Sociales Salé, Université Mohammed V de Rabat, Salé, Morocco ' Département de Mathématiques, Université Chouaib Doukkali, El Jadida, Morocco ' Département de Mathématiques, Université Chouaib Doukkali, El Jadida, Morocco
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.
Keywords: compound matrix; generalized incidence function; geometric approach; global asymptotic stability; SEIR epidemic model; vertical transmission.
International Journal of Dynamical Systems and Differential Equations, 2017 Vol.7 No.3, pp.217 - 228
Received: 26 Aug 2016
Accepted: 19 Nov 2016
Published online: 08 Sep 2017 *