Skip to Main content Skip to Navigation
Journal articles

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
2 LANI
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.
Complete list of metadata

Cited literature [19 references]  Display  Hide  Download

https://hal.inria.fr/hal-01086101
Contributor : Abderrahman Iggidr <>
Submitted on : Friday, November 21, 2014 - 11:23:29 PM
Last modification on : Tuesday, March 2, 2021 - 5:12:05 PM
Long-term archiving on: : Friday, April 14, 2017 - 8:13:02 PM

File

213-1968-1-PB.pdf
Publisher files allowed on an open archive

Identifiers

Collections

Citation

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⟩

Share

Metrics

Record views

637

Files downloads

489