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Global stability of an epidemic model with two infected stages and mass-action incidence

Mamadou Lamine Diouf 1, 2 Abderrahman Iggidr 1, 3 Mamadou Sy 2 
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
LANI - Laboratoire d'Analyse Numérique et Informatique [Sénégal]
Abstract : —The goal of this paper is the establishment of the global asymptotic stability of the model SI with two classes of infected stages and with varying total population size. The incidence used is the mass-action incidence given by (β 1 I 1 + β 2 I 2) S /N . Existence and uniqueness of the endemic equilibrium is established when the basic reproduction number is greater than one. A Lyapunov function is used to prove the stability of the disease free equilibrium, and the Poincarré-Bendixson theorem allows to prove the stability of the endemic equilibrium when it exists.
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Submitted on : Friday, November 21, 2014 - 11:23:29 PM
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Mamadou Lamine Diouf, Abderrahman Iggidr, Mamadou Sy. Global stability of an epidemic model with two infected stages and mass-action incidence. BIOMATH, Biomath Forum, 2014, 3 (1), pp.1--8. ⟨10.11145/j.biomath.2014.07.211⟩. ⟨hal-01086101⟩



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