Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 23, pp. 1-13.

Title: Global stability for delay SIR and SEIR epidemic models with
       saturated incidence rates

Authors: Abdelhadi Abta (Faculte des Sciences, El Jadida, Morocco)
         Abdelilah Kaddar (Univ. Mohammed V- Souissi, Morocco)
	 Hamad Talibi Alaoui (Faculte des Sciences, El Jadida, Morocco)

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 07, 2012.
Math Subject Classifications: 34D23, 37B25, 00A71.
Key Words: SIR epidemic model; SEIR epidemic model; incidence rate;
           delay differential equations; Lyapunov function; global stability.