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Mathematical Biosciences and Engineering (MBE)
 

A bacteriophage model based on CRISPR/Cas immune system in a chemostat

Pages: 1361 - 1377, Volume 14, Issue 5/6, October/December 2017      doi:10.3934/mbe.2017070

 
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Mengshi Shu - Key Laboratory of Eco-environments in Three Gorges Reservoir Region, School of Mathematics and Statistics, Southwest University, Chongqing 400715, China (email)
Rui Fu - Key Laboratory of Eco-environments in Three Gorges Reservoir Region, School of Mathematics and Statistics, Southwest University, Chongqing 400715, China (email)
Wendi Wang - Key Laboratory of Eco-environments in Three Gorges Reservoir Region, School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China (email)

Abstract: Clustered regularly interspaced short palindromic repeats(CRISPRs) along with Cas proteins are a widespread immune system across bacteria and archaea. In this paper, a mathematical model in a chemostat is proposed to investigate the effect of CRISPR/Cas on the bacteriophage dynamics. It is shown that the introduction of CRISPR/Cas can induce a backward bifurcation and transcritical bifurcation. Numerical simulations reveal the coexistence of a stable infection-free equilibrium with an infection equilibrium, or a stable infection-free equilibrium with a stable periodic solution.

Keywords:  Bacteriophage, bifurcation, bistability, backward, evolution.
Mathematics Subject Classification:  Primary: 92D30; Secondary: 34D20.

Received: May 2016;      Accepted: November 2016;      Available Online: May 2017.

 References