| Issue |
ESAIM: Proc.
Volume 39, March 2013
Conference on Structural Nonlinear Dynamics and Diagnosis – CSNDD 2012
|
|
|---|---|---|
| Page(s) | 1 - 6 | |
| DOI | https://doi.org/10.1051/proc/201339001 | |
| Published online | 14 May 2013 | |
Global Analysis for a Delay-Distributed SIR Epidemic Model
1 Université Chouaib Doukkali,
FS, BP.20,
El Jadida,
Morocco
2 Université Ibn Tofail, FS, LIRNE, BP. 133, Kénitra,
Morocco
3 Université Mohammed V-Souissi,
FSEJS, BP. 5285,
Salé,
Morocco
One of the most tools for describing the incubation period in the epidemiological dynamic models is the distributed delays. In this paper, we propose a delay-distributed SIR epidemic model with a nonlinear incidence rate. Using the Lyapunov theory and LaSalle’s principle, we show the global asymptotic stability of the disease-free and the endemic equilibria. This analysis extends and performs existing results.
Résumé
En épidémiologie le retard joue un rôle très important dans la représentation de la période d’incubation. Dans ce travail, nous étudions un modèle SIR à retard distribué, avec une fonction d’incidence non linéaire. Pour analyser la stabilité globale du point d’équilibre sans maladie et du point d’équilibre endémique, nous utilisons la théorie de Lyapunov et le principe d’invariance de LaSalle.
© EDP Sciences, SMAI 2013
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