Pour une classe générale de modèles, nous prouvons la globale asymptotique stabilité de l'équilibre sans maladie sous des hypothèses générales. Ces conditions sont relatives au nombre de reproduction de base . Nous donnons également un algorithme pratique permettant d'établir une condition de seuil équivalente à . Nous montrons que ces deux résultats peuvent être appliqués à de nombreux modèles épidémiologiques de la littérature.
For a general class of models, we prove the global asymptotic stability (GAS) of the disease free equilibrium (DFE) under general assumptions. These conditions are related to the basic reproductive ratio . We also give a practical algorithm to compute a threshold condition equivalent to . We show that these two results can be applied to numerous epidemiological models from the literature.
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@article{CRMATH_2005__341_7_433_0, author = {Kamgang, Jean Claude and Sallet, Gauthier}, title = {Global asymptotic stability for the disease free equilibrium for epidemiological models}, journal = {Comptes Rendus. Math\'ematique}, pages = {433--438}, publisher = {Elsevier}, volume = {341}, number = {7}, year = {2005}, doi = {10.1016/j.crma.2005.07.015}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.07.015/} }
TY - JOUR AU - Kamgang, Jean Claude AU - Sallet, Gauthier TI - Global asymptotic stability for the disease free equilibrium for epidemiological models JO - Comptes Rendus. Mathématique PY - 2005 SP - 433 EP - 438 VL - 341 IS - 7 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.07.015/ DO - 10.1016/j.crma.2005.07.015 LA - en ID - CRMATH_2005__341_7_433_0 ER -
%0 Journal Article %A Kamgang, Jean Claude %A Sallet, Gauthier %T Global asymptotic stability for the disease free equilibrium for epidemiological models %J Comptes Rendus. Mathématique %D 2005 %P 433-438 %V 341 %N 7 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.07.015/ %R 10.1016/j.crma.2005.07.015 %G en %F CRMATH_2005__341_7_433_0
Kamgang, Jean Claude; Sallet, Gauthier. Global asymptotic stability for the disease free equilibrium for epidemiological models. Comptes Rendus. Mathématique, Tome 341 (2005) no. 7, pp. 433-438. doi : 10.1016/j.crma.2005.07.015. http://archive.numdam.org/articles/10.1016/j.crma.2005.07.015/
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