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Stability analysis and dynamics preserving nonstandard finite difference schemes for a malaria model

Anguelov R., Dumont Y., Lubuma J., Mureithi E.. 2013. Mathematical Population Studies, 20 (2) : p. 101-122.

When both human and mosquito populations vary, forward bifurcation occurs if the basic reproduction number R0 is less than one in the absence of disease-induced death. When the disease-induced death rate is large enough, R0¼1 is a subcritical backward bifurcation point. The domain for the study of the dynamics is reduced to a compact and feasible region, where the system admits a specific algebraic decomposition into infective and non-infected humans and mosquitoes. Stability results are extended and the possibility of backward bifurcation is clarified. A dynamically consistent nonstandard finite difference scheme is designed. (Résumé d'auteur)

Mots-clés : santé publique; Épidémiologie; malaria; anopheles; dynamique des populations; contrôle de maladies; modèle de simulation; modèle mathématique; afrique du sud

Thématique : Méthodes mathématiques et statistiques; Maladies des animaux; Organismes nuisibles des animaux; Autres thèmes

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