Geodesic
Global Analysis for a Delay-Distributed SIR Epidemic Model
Abdelhadi Abta1 ; Mohamed El Fatini2 ; Soufiane Elkhaiar1 ; Abdelilah Kaddar3
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
ESAIM. Proceedings, Tome 39 (2013), pp. 1-6.

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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.
DOI : 10.1051/proc/201339001

Abdelhadi Abta 1 ; Mohamed El Fatini 2 ; Soufiane Elkhaiar 1 ; Abdelilah Kaddar 3

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 
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     title = {Global {Analysis} for a {Delay-Distributed} {SIR} {Epidemic} {Model}},
     journal = {ESAIM. Proceedings},
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     doi = {10.1051/proc/201339001},
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Abdelhadi Abta; Mohamed El Fatini; Soufiane Elkhaiar; Abdelilah Kaddar. Global Analysis for a Delay-Distributed SIR Epidemic Model. ESAIM. Proceedings, Tome 39 (2013), pp. 1-6. doi : 10.1051/proc/201339001. http://geodesic.mathdoc.fr/articles/10.1051/proc/201339001/

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