STABILITY ANALYSIS OF AN SEIR MODEL WITH VACCINATION

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Published: 2015-10-08

Page: 92-102


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


How to Cite

ELKHAIAR, S., KADDAR, A., & ELADNANI, F. (2015). STABILITY ANALYSIS OF AN SEIR MODEL WITH VACCINATION. Asian Journal of Mathematics and Computer Research, 8(2), 92–102. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/492

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