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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 320581, 10 pages
http://dx.doi.org/10.1155/2013/320581
Research Article

Analysis of a Dengue Disease Model with Nonlinear Incidence

1Department of Mathematics and Information Science, Shaoguan University, Shaoguan 512005, China
2Department of Mathematics, Xinyang Normal University, Xinyang 464000, China
3School of Advanced Sciences, VIT University, Chennai Campus, Chennai 600048, India

Received 10 September 2012; Revised 3 January 2013; Accepted 3 January 2013

Academic Editor: Eric Campos Canton

Copyright © 2013 Shu-Min Guo 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

A dengue disease epidemic model with nonlinear incidence is formulated and analyzed. The equilibria and threshold of the model are found. The stability of the system is analyzed through a geometric approach to stability. The proposed model also exhibits backward bifurcation under suitable conditions on parameters. Our results imply that a nonlinear incidence produces rich dynamics and they should be studied carefully in order to analyze the spread of disease more accurately. Finally, numerical simulations are presented to illustrate the analytical findings.