Abdelhadi Abta, Abdelilah Kaddar, Hamad Talibi Alaoui
Abstract:
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.
Submitted October 31, 2011. Published February 7, 2012.
Math Subject Classifications: 34D23, 37B25, 00A71.
Key Words: SIR epidemic model; SEIR epidemic model; incidence rate;
delay differential equations; Lyapunov function; global stability.
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Abdelhadi Abta Chouaib Doukkali, Faculté des Sciences Département de Mathématiques et Informatique B.P. 20, El Jadida, Morocco email: abtaabdelhadi@yahoo.fr |
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Abdelilah Kaddar Université Mohammed V- Souissi Faculté des Sciences Juridiques, Economiques et Sociales - Salé, Morocco email: a.kaddar@yahoo.fr |
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Hamad Talibi Alaoui Chouaib Doukkali, Faculté des Sciences Département de Mathématiques et Informatique B.P. 20, El Jadida, Morocco email: talibi_1@hotmail.fr |
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