Modeling and analysis of a marine bacteriophage infection with latency period.

*(English)*Zbl 1015.92049From the paper: We propose a delay differential equation model which describes the bacteriophage infection of marine bacteria in the thermoclinic level of the sea during the warm season; the experimental evidence has been reported by several authors. We describe the time evolution of three population densities (assumed spatially homogeneous), namely the susceptible bacteria, the phage-infected bacteria and the infecting agent: the phages. One goal of the authors in this paper is that of providing a better description of the infected class of bacteria with respect to their previous model in Math. Biosci. 149, No. 1, 57-76 (1998; Zbl 0946.92012), where the infection was described by a system of three nonlinear ODEs.

##### MSC:

92D40 | Ecology |

34K60 | Qualitative investigation and simulation of models involving functional-differential equations |

34K20 | Stability theory of functional-differential equations |

##### Keywords:

time delays; Lyapunov functionals; global stability; persistence; bacteriophage infection; marine bacteria
PDF
BibTeX
XML
Cite

\textit{E. Beretta} and \textit{Y. Kuang}, Nonlinear Anal., Real World Appl. 2, No. 1, 35--74 (2001; Zbl 1015.92049)

Full Text:
DOI

##### References:

[1] | Anderson, R.M.; May, R.M., The population dynamics of microparasites and their invertebrate hosts, Proc. roy. soc. lond., B291, 451-524, (1981) |

[2] | Barbǎlat, I., Systemes d’equations differentielles d’oscillations non lineares, Rev. math. pure et appl., 4, 267-270, (1959) · Zbl 0090.06601 |

[3] | Bergh, O.; Borsheim, K.Y.; Bratback, G.; Heldal, M., High abundance of viruses found in aquatic environments, Nature, 340, 467-468, (1989) |

[4] | Beretta, E.; Kuang, Y., Modeling and analysis of a marine bacteriophage infection, Math. biosc., 149, 57-76, (1998) · Zbl 0946.92012 |

[5] | Bremermann, H.J., Parasites at the origin of life, J. math. biol., 16, 165-180, (1983) · Zbl 0498.92002 |

[6] | Campbell, A., Conditions for the existence of bacteriophage, Evolution, 15, 153-165, (1961) |

[7] | Cooke, K.; Kuang, Y.; Li, B., Analysis of an antiviral immune response model with time delays, Can. appl. math. quart., 6, 321-354, (1998) · Zbl 0941.92015 |

[8] | Freedman, H.I.; Waltman, P., Persistence in models of three interacting predator-prey populations, Math. biosc., 68, 213-231, (1984) · Zbl 0534.92026 |

[9] | Y. Kuang, Delay Differential Equations, with Applications in Population Dynamics, Academic Press, New York, 1993. · Zbl 0777.34002 |

[10] | Lenski, R.E.; Levin, B.R., Constraints on the coevolution of bacteria and virulent phage: a model, some experiments, and predictions for natural communities, Amer. naturalist, 125, 585-602, (1985) |

[11] | Moebus, K., Lytic and inhibition responses to bacteriophages among marine bacteria, with special reference to the origin of phage-host systems, Helgolander meeresuntersuchungen, 36, 375, (1983) |

[12] | Proctor, L.M.; Fuhrman, J.A., Viral mortality of marine bacteria and cyanobacteria, Nature, 343, 60-62, (1990) |

[13] | Proctor, L.M.; Okubo, A.; Fuhrman, J.A., Calibrating of phage-induced mortality in marine bacteria. ultrastructural studies of marine bacteriophage development from one-step growth experiments, Microb. ecol., 25, 161-182, (1993) |

[14] | J. Sieburth, Sea Microbes, Oxford University Press, New York, 1979. |

[15] | Thieme, H.R., Persistence under relaxed point-dissipativity (with application to an endemic model), SIAM J. math. anal., 24, 407-435, (1993) · Zbl 0774.34030 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.