On the dynamics of a class of multi-group models for vector-borne diseases

Abstract : The resurgence of vector-borne diseases is an increasing public health concern, and there is a need for a better understanding of their dynamics. For a number of diseases, e.g. dengue and chikungunya, this resurgence occurs mostly in urban environments, which are naturally very heterogeneous, particularly due to population circulation. In this scenario, there is an increasing interest in both multi-patch and multi-group models for such diseases. In this work, we study the dynamics of a vector borne disease within a class of multi-group models that extends the classical Bailey-Dietz model. This class includes many of the proposed models in the literature, and it can accommodate various functional forms of the infection force. For such models, the vector-host/host-vector contact network topology gives rise to a bipartite graph which has different properties from the ones usually found in directly transmitted diseases. Under the assumption that the contact network is strongly connected, we can define the basic reproductive number R 0 and show that this system has only two equilibria: the so called disease free equilibrium (DFE); and a unique interior equilibrium—usually termed the endemic equilibrium (EE)—that exists if, and only if, R 0 > 1. We also show that, if R 0 ≤ 1, then the DFE equilibrium is globally asymptotically stable, while when R 0 > 1, we have that the EE is globally asymptotically stable.
Type de document :
Article dans une revue
Journal of Mathematical Analysis and applications, Elsevier, 2016, 〈10.1016/j.jmaa.2016.04.003〉
Liste complète des métadonnées

Littérature citée [86 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01249798
Contributeur : Abderrahman Iggidr <>
Soumis le : mardi 3 mai 2016 - 17:37:36
Dernière modification le : jeudi 11 janvier 2018 - 06:26:21
Document(s) archivé(s) le : mardi 15 novembre 2016 - 19:55:50

Fichier

MGVB_Dynamics-cor.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Abderrahman Iggidr, Gauthier Sallet, Max O. Souza. On the dynamics of a class of multi-group models for vector-borne diseases. Journal of Mathematical Analysis and applications, Elsevier, 2016, 〈10.1016/j.jmaa.2016.04.003〉. 〈hal-01249798v2〉

Partager

Métriques

Consultations de la notice

116

Téléchargements de fichiers

72