A TIME DELAY MODEL FOR BACTERIA BACTERIOPHAGE INTERACTION

Abstract

A continuous delay differential model for dynamics of bacteria and bacteriophage interaction has been developed. The time lag is assumed because of latency period of infected bacteria. The model incorporates the lysogenic life cycle of bacteriophage. Accordingly, the infected bacteria can grow logistically. Due to the presence of lytic phage inside the infected bacterium cell, a constant number of phage is released to the system after lysis of each infected bacteria. The model has been analyzed both analytically and numerically. The coexistence of bacteria, bacteriophage and infected bacteria has been established. The condition for existence and stability of susceptible bacteria free equilibrium has been obtained. A simple Hopf-bifurcation has been discussed for non-zero equilibrium point. The lysogenic growth of infected bacteria can stabilize the unstable positive equilibrium point and increases the region of stability. Further, the unstable disease free equilibrium state can be stabilized with inclusion of lysogenic growth.