Geodesic
Global stability for delay SIR and SEIR epidemic models with saturated incidence rates
Electronic journal of differential equations, Tome 2012 (2012)
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},
     year = {2012},
     volume = {2012},
     zbl = {1243.34115},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a18/}
}
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AU  - Kaddar,  Abdelilah
AU  - Alaoui,  Hamad Talibi
TI  - Global stability for delay SIR and SEIR epidemic models with saturated incidence rates
JO  - Electronic journal of differential equations
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VL  - 2012
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%A Abta,  Abdelhadi
%A Kaddar,  Abdelilah
%A Alaoui,  Hamad Talibi
%T Global stability for delay SIR and SEIR epidemic models with saturated incidence rates
%J Electronic journal of differential equations
%D 2012
%V 2012
%U http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a18/
%G en
%F EJDE_2012__2012__a18
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/