—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.
Publié le : 2014-07-04
Classification:
Mass-action incidence,
Global stability,
-Epidemic model,
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS],
[SDV.SPEE]Life Sciences [q-bio]/Santé publique et épidémiologie
@article{hal-01086101,
author = {Lamine Diouf, Mamadou and Iggidr, Abderrahman and Sy, Mamadou},
title = {Global stability of an epidemic model with two infected stages and mass-action incidence},
journal = {HAL},
volume = {2014},
number = {0},
year = {2014},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01086101}
}
Lamine Diouf, Mamadou; Iggidr, Abderrahman; Sy, Mamadou. Global stability of an epidemic model with two infected stages and mass-action incidence. HAL, Tome 2014 (2014) no. 0, . http://gdmltest.u-ga.fr/item/hal-01086101/