STABILITY ANALYSIS OF AN SEIR MODEL WITH VACCINATION
SOUFIANE ELKHAIAR
Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University, P.O.Box 20, ElJadida, Morocco
ABDELILAH KADDAR *
Department of Economics, Faculty of Juridical, Economic and Social Sciences of Sale, Mohammed V University in Rabat, P.O.Box 8007, Rabat, Morocco
FATIHA ELADNANI
Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University, P.O.Box 20, ElJadida, Morocco
*Author to whom correspondence should be addressed.
Abstract
In this paper an SEIR epidemic model with vaccination is investigated. It is assumed that the incidence is a general nonlinear function. Lyapunov's method, Hurwitz's criterion and Li's geometrical approach are used to study the dynamic behavior of the possible equilibria: the disease-free equilibrium and the endemic equilibrium. The e ect of vaccination rate can be easily seen on the reproduction number R0 and consequently on the existence of the endemic equilibrium. Further, the reproduction number plays a big role on the stability analysis: if R0 1, the disease-free equilibrium is proven to be globally asymptotically stable and the disease dies out, while if R0 > 1, the endemic equilibrium is shown to be globally asymptotically stable in the interior of the feasible region.
Keywords: SEIR epidemic model, generalized incidence rates, global asymptotic stability, vaccination, Lyapunov-LaSalle's principle, geometric approach, compound matrix