MODELING AND ANALYSIS OF A MARINE BACTERIOPHAGE INFECTION

A mathematical model for the marine bacteriophage infection is propose d and its essential mathematical features are analyzed. Since bacterio phage infection induces bacterial lysis which releases into the marine environment, on the average, 'b' viruses per cell, the parameter b ep silon (1, + infinity) or 'virus replication factor' is chosen as the m ain parameter an which the dynamics of the infection depends. We prove d that a threshold b exists beyond which the endemic equilibrium bifu rcates from the free disease one. Still, for increasing b values the e ndemic equilibrium bifurcates toward a periodic solution. We proved th at a compact attractor set Omega within the positive cone exists and w ithin Omega the free disease equilibrium is globally stable whenever b less than or equal to b, whereas it becomes a strong uniform repelle r for b > b, A concluding discussion with numerical simulation is the n presented. (C) 1998 Elsevier Science Inc. All rights reserved.