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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 Contributor : Abderrahman IggidrConnect in order to contact the contributor Submitted on : Monday, December 30, 2013 - 11:03:40 PM Last modification on : Saturday, June 25, 2022 - 7:46:54 PM Long-term archiving on: : Sunday, March 30, 2014 - 10:31:02 PM
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⟩