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

Authors
Journal
Computers & Mathematics with Applications
0898-1221
Publisher
Elsevier
Publication Date
Volume
56
Issue
11
Identifiers
DOI: 10.1016/j.camwa.2008.09.019
Keywords
  • Quorum Sensing
  • Immunity
  • Periodic Solution
  • Stability
  • Subharmonic Bifurcation
  • Perturbation

Abstract

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.

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