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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Jean Claude Kamgang 1 ; Gauthier Sallet 2
@article{CRMATH_2005__341_7_433_0, author = {Jean Claude Kamgang and Gauthier Sallet}, 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}, }
TY - JOUR AU - Jean Claude Kamgang AU - Gauthier Sallet 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 DO - 10.1016/j.crma.2005.07.015 LA - en ID - CRMATH_2005__341_7_433_0 ER -
Jean Claude Kamgang; Gauthier Sallet. Global asymptotic stability for the disease free equilibrium for epidemiological models. Comptes Rendus. Mathématique, Volume 341 (2005) no. 7, pp. 433-438. doi : 10.1016/j.crma.2005.07.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.07.015/
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