Modeling and analysis of a marine bacteriophage infection

A mathematical model for the marine bacteriophage infection is proposed and its essential mathematical features are analyzed. Since bacteriophage infection induces bacterial lysis which releases into the marine environment, on the average, `bʹ viruses per cell, the parameter b∈(1,+∞) or `virus replication factorʹ is chosen as the main parameter on which the dynamics of the infection depends. We proved that a threshold b∗ exists beyond which the endemic equilibrium bifurcates from the free disease one. Still, for increasing b values the endemic equilibrium bifurcates toward a periodic solution. We proved that a compact attractor set Ω within the positive cone exists and within Ω the free disease equilibrium is globally stable whenever b⩽b∗, whereas it becomes a strong uniform repeller for b>b∗. A concluding discussion with numerical simulation is then presented.