We give a survey of results on global stability for deterministic compartmental epidemiological models. Using Lyapunov techniques we revisit a classical result, and give a simple proof. By the same methods we also give a new result on differential susceptibility and infectivity models with mass action and an arbitrary number of compartments. These models encompass the so-called differential infectivity and staged progression models. In the two cases we prove that if the basic reproduction ratio R0 \leq 1, then the disease free equilibrium is globally asymptotically stable. If R0 > 1, there exists an unique endemic equilibrium which is asymptotically stable on the positive orthant.
Publié le : 2007-07-05
Classification:
Differential susceptibility models,
Nonlinear dynamical systems,
Global stability,
Lyapunov methods,
Differential susceptibility models.,
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS],
[SDV.SPEE]Life Sciences [q-bio]/Santé publique et épidémiologie
@article{inria-00596236,
author = {A. Fall, A. and Iggidr, Abderrahman and Sallet, Gauthier and Tewa, Jean-Jules},
title = {Epidemiological models and Lyapunov functions},
journal = {HAL},
volume = {2007},
number = {0},
year = {2007},
language = {en},
url = {http://dml.mathdoc.fr/item/inria-00596236}
}
A. Fall, A.; Iggidr, Abderrahman; Sallet, Gauthier; Tewa, Jean-Jules. Epidemiological models and Lyapunov functions. HAL, Tome 2007 (2007) no. 0, . http://gdmltest.u-ga.fr/item/inria-00596236/