# American Institute of Mathematical Sciences

September  2015, 20(7): 2217-2232. doi: 10.3934/dcdsb.2015.20.2217

## Global stability of the dengue disease transmission models

 1 School of Science, Xi'an University of Architecture & Technology, Xi'an, 710055, China 2 Department of Mathematics, Xinyang Normal University, Xinyang 464000, China

Received  January 2015 Revised  May 2015 Published  July 2015

In this paper, we further investigate the global stability of the dengue transmission models. By using persistence theory, it is showed that the disease of system uniformly persists when the basic reproduction number is larger than unity. By constructing suitable Lyapunov function methods and LaSalle Invariance Principle, we show that the unique endemic equilibrium of the model is always globally asymptotically stable as long as it exists.
Citation: Jing-Jing Xiang, Juan Wang, Li-Ming Cai. Global stability of the dengue disease transmission models. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2217-2232. doi: 10.3934/dcdsb.2015.20.2217
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