Analysis of a bacteria–immunity model with delay quorum sensing

A bacteria–immunity model with bacterial quorum sensing is formulated, which describes the competition between bacteria and immune cells. A distributed delay is introduced to characterize the time in which bacteria receive signal molecules and then combat with immune cells. In this paper, we focus on a subsystem of the bacteria–immunity model, analyze the stability of the equilibrium points, discuss the existence and stability of periodic solutions bifurcated from the positive equilibrium point, and finally investigate the stability of the nonhyperbolic equilibrium point by the center manifold theorem.