Journal of Applied Mathematics
Volume 2012 (2012), Article ID 342472, 11 pages
http://dx.doi.org/10.1155/2012/342472
Research Article

Global Stability of Multigroup Dengue Disease Transmission Model

Deqiong Ding,1 Xueping Wang,2 and Xiaohua Ding1

1Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China
2Department of Education, Urumqi Vocational University, Urumqi 830002, China

Received 10 November 2011; Accepted 2 January 2012

Academic Editor: Jitao Sun

Copyright © 2012 Deqiong Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate a class of multigroup dengue epidemic model. We show that the global dynamics are determined by the basic reproductive number 𝑅 0 . We present that when 𝑅 0 ≤ 1 , there is a unique disease-free equilibrium which is globally asymptotically stable; when 𝑅 0 > 1 , there exists a unique endemic equilibrium and it is globally asymptotically stable proved by a graph-theoretic approach to the method of global Lyapunov function.