Some new results on an allelopathic competition model with quorum sensing and delayed toxicant production

A bacteria-immunity system with delayed quorum sensing

“…Similar to Lemma 1 in [10], we easily prove that the solution of system (1) remains positive whenever it exists.…”

“…Recently, quorum sensing mechanism has been paid more and more attention by biomathematics scholars, and quite a few mathematical models have been formulated (see, for example, [1,[9][10][11] and references therein). Obviously, new models which characterizes this mechanism from different views are extremely needed.…”

Stability and Sensitive Analysis of a Model with Delay Quorum Sensing

“…Now, many other species are observed to exhibit quorum sensing behavior, including major human pathogens such as Staphylococcus aureus and Pseudomonas aeruginosa. Quorum sensing has received more and more attention (see [4][5][6][7][8][9][10][11][12][13][14][15] and the references therein) and some models are formulated to investigate its effect on the transmission of disease. Braselton and Waltman [4] formulated the dynamically allocated inhibitor production.…”

“…They gave some sufficient conditions for the global asymptotic stability of two boundary equilibria which, respectively, correspond to the survival of the allelochemical producer species or the susceptible one. Fergola et al [7] formulated an allelopathic competition model in which a distributed delay term simulates quorum sensing which regulates the delay production process of allelochemicals, and they proved the unique existence of the positive solution and the stability of biologically meaningful steady-state solutions. Anguige et al [9] constructed a multiphase mathematical model of quorum sensing in a maturing Pseudomonas aeruginosa biofilm to investigate the effect of antiquorum sensing and antibiotic treatments on the exopolysaccharide concentration, signal level, bacterial numbers, and biofilm growth rate.…”

On the dynamical behavior of some algal allelopathic competitions in chemostat-like environment

“…To represent this type of competition a mathematical model has been suggested in [19,20] by Waltman, Braselton and Shu and adopted in [21][22][23][24] to study some bacterial competitions.…”