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Abstract and Applied Analysis
Volume 2015, Article ID 964735, 11 pages
Research Article

Stability and Sensitive Analysis of a Model with Delay Quorum Sensing

1School of Science, Xi’an University of Science and Technology, Xi’an, Shaanxi 710054, China
2Department of Mathematics, North China Electric Power University, Beijing 102206, China

Received 26 August 2014; Accepted 17 December 2014

Academic Editor: Yanni Xiao

Copyright © 2015 Zhonghua Zhang 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.


This paper formulates a delay model characterizing the competition between bacteria and immune system. The center manifold reduction method and the normal form theory due to Faria and Magalhaes are used to compute the normal form of the model, and the stability of two nonhyperbolic equilibria is discussed. Sensitivity analysis suggests that the growth rate of bacteria is the most sensitive parameter of the threshold parameter and should be targeted in the controlling strategies.