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

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.