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

  • Received: 31 May 2016 Accepted: 21 November 2016 Published: 01 October 2017
  • MSC : Primary: 92D30; Secondary: 34D20

  • 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.

    Citation: Mengshi Shu, Rui Fu, Wendi Wang. A bacteriophage model based on CRISPR/Cas immune system in a chemostat[J]. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1361-1377. doi: 10.3934/mbe.2017070

    Related Papers:

  • 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.
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    © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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