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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:441

Article

Iggidr, Aberrahman¹  Sallet, Gauthier¹  Souza, Max O.² 

[1] Univ Lorraine, CNRS, Inria, Inst Elie Cartan Lorraine,UMR 7502, ISGMP Bat A, F-57045 Metz 01, France

[2] Univ Fed Fluminense, Dept Matemat Aplicada, R Mario Santos Braga S-N, BR-24020140 Niteroi, RJ, Brazil

关键词: Vector-borne diseases;    Metzler matrix;    Network models;    Global stability;    Lyapunov functions;    Multigraphs;   

DOI  :  10.1016/j.jmaa.2016.04.003

来源: Elsevier

【 摘 要 】

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 BE is globally asymptotically stable. (c) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free