Geodesic
Global stability for delay SIR and SEIR epidemic models with saturated incidence rates
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this article we propose a comparison of a delayed SIR model and its corresponding SEIR model in terms of global stability. We consider a saturated incidence rate and we determine, using Lyapunov functionals, conditions by which the disease-free equilibrium and the endemic equilibrium are globally asymptotically stable. Also some numerical simulations are given to compare a global behaviour of a delayed SIR model and its corresponding SEIR model.
Classification : 34D23, 37B25, 00A71
Keywords: SIR epidemic model, SEIR epidemic model, incidence rate, delay differential equations, Lyapunov function, global stability 
@article{EJDE_2012__2012__a18,
     author = {Abta, Abdelhadi and Kaddar, Abdelilah and Alaoui, Hamad Talibi},
     title = {Global stability for delay {SIR} and {SEIR} epidemic models with saturated incidence rates},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a18/}
}
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Abta, Abdelhadi; Kaddar, Abdelilah; Alaoui, Hamad Talibi. Global stability for delay SIR and SEIR epidemic models with saturated incidence rates. Electronic Journal of Differential Equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a18/