# Global stability of a SI epidemic model with two infected stages and mass-action incidence

* Corresponding author
1 MASAIE - Tools and models of nonlinear control theory for epidemiology and immunology
LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
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.
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Cited literature [13 references]

https://hal.inria.fr/hal-00922831
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Submitted on : Monday, December 30, 2013 - 11:03:40 PM
Last modification on : Tuesday, March 2, 2021 - 5:12:05 PM
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• HAL Id : hal-00922831, version 1

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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⟩

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