IECL - Institut Élie Cartan de Lorraine (Université de Lorraine, Boulevard des Aiguillettes BP 70239 54506 Vandoeuvre-les-Nancy Cedex
Ile du Saulcy - 57 045 Metz Cedex 01 - France)
IECL - Institut Élie Cartan de Lorraine (Université de Lorraine, Boulevard des Aiguillettes BP 70239 54506 Vandoeuvre-les-Nancy Cedex
Ile du Saulcy - 57 045 Metz Cedex 01 - France)
Abstract : The work done in this paper consists in the establishment of the global stability of the model SI containing two classes of infected stages. The incidence used is non-linear and given by $(\beta_1 I_1+\beta_2 I_2)\dfrac{S}{N}$.\\ Existence and uniqueness of the endemic equilibrium is established. A Lyapunov function is used to prove the stability of the disease free equilibrium, and the Poincarré-Bendixson theorem allows to prove the global asymptotic stability of the endemic equilibrium when it exists.
https://hal.inria.fr/hal-00922831
Contributeur : Abderrahman Iggidr
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Soumis le : lundi 30 décembre 2013 - 23:03:40
Dernière modification le : jeudi 11 janvier 2018 - 06:26:21
Document(s) archivé(s) le : dimanche 30 mars 2014 - 22:31:02
Mamadou Lamine Diouf, Abderrahman Iggidr, Mamadou Sy. Global stability of a SI epidemic model with two infected stages and mass-action incidence. [Research Report] RR-8441, INRIA. 2013, pp.13. 〈hal-00922831〉
