Analysis of a periodic bacteria-immunity model with delayed quorum sensing

  • Authors:

  • Zhonghua Zhang;Yaohong Suo;Jigeng Peng;Juan Zhang

  • Affiliations:

  • School of Sciences, Xi'an University of Science and Technology, Xi'an 710054, China;School of Sciences, Xi'an University of Science and Technology, Xi'an 710054, China;Research Center for Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, China;Department of Mathematics, North China Electric Power University, Beijing, 102206, China

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2008

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Abstract

Based on [J. Zhang, M. Cerasuolo, P. Fergola, Z.E. Ma, On the influence of quorum sensing in the competition between bacteria and immune system (in press)], a bacteria-immunity model with periodically bacterial quorum sensing is formulated which describes the competition between bacteria and immune cells. A discrete delay is introduced to characterize the time in which bacteria receive signal molecules and combat with immune cells. In this paper, we focus on a subsystem of the bacteria-immunity model, investigate the existence and stability of the positively periodic solution, and discuss the existence of subharmonic bifurcation by the perturbation method.