Dynamics of a Ratio-Dependent Marine Bacteriophage Infection Model with Delay

Abstract

A three dimensional mathematical model is considered to investigate the effect of virus infection in bacterial community. Due to virus infection the bacteria population is divided into susceptible class and infected class. The model is formulated by considering logistic growth of the susceptible class and a standard incidence function governing viral infection. The model is modified by considering an explicit time delay in virus production. The basic demographic reproductive number Rd, the basic epidemiological reproductive number R0 are used in qualitative analysis. We show that when R0 > 1, there exists a biologically meaningful steady state and the stability of this steady state is dependent upon both Rd and R0. Comparative study of models with delay and without delay are carried out both analytically and numerically.