Modeling and analysis of a marine bacteriophage infection

Edoardo Beretta, Yang Kuang

Research output: Contribution to journalArticle

111 Citations (Scopus)

Abstract

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, 'b' viruses per cell, the parameter b ε (l, + oo) or 'virus replication factor' 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.

Original languageEnglish (US)
Pages (from-to)57-76
Number of pages20
JournalMathematical Biosciences
Volume149
Issue number1
DOIs
StatePublished - Apr 1998

Fingerprint

Bacteriophages
bacteriophage
Viruses
bacteriophages
Infection
Endemic Equilibrium
Virus
virus
Virus Replication
virus replication
bacterial infections
Modeling
Bacterial Infections
marine environment
infection
modeling
Cones
Positive Cone
Theoretical Models
mathematical models

Keywords

  • Global stability
  • Hopf bifurcation
  • Marine bacteriophage infection
  • Persistence
  • Strong uniform repeller

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics

Cite this

Modeling and analysis of a marine bacteriophage infection. / Beretta, Edoardo; Kuang, Yang.

In: Mathematical Biosciences, Vol. 149, No. 1, 04.1998, p. 57-76.

Research output: Contribution to journalArticle

@article{6aba3c2bc3e14b81b8fced0f9358e5c6,
title = "Modeling and analysis of a marine bacteriophage infection",
abstract = "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, 'b' viruses per cell, the parameter b ε (l, + oo) or 'virus replication factor' 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.",
keywords = "Global stability, Hopf bifurcation, Marine bacteriophage infection, Persistence, Strong uniform repeller",
author = "Edoardo Beretta and Yang Kuang",
year = "1998",
month = "4",
doi = "10.1016/S0025-5564(97)10015-3",
language = "English (US)",
volume = "149",
pages = "57--76",
journal = "Mathematical Biosciences",
issn = "0025-5564",
publisher = "Elsevier Inc.",
number = "1",

}

TY - JOUR

T1 - Modeling and analysis of a marine bacteriophage infection

AU - Beretta, Edoardo

AU - Kuang, Yang

PY - 1998/4

Y1 - 1998/4

N2 - 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, 'b' viruses per cell, the parameter b ε (l, + oo) or 'virus replication factor' 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.

AB - 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, 'b' viruses per cell, the parameter b ε (l, + oo) or 'virus replication factor' 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.

KW - Global stability

KW - Hopf bifurcation

KW - Marine bacteriophage infection

KW - Persistence

KW - Strong uniform repeller

UR - http://www.scopus.com/inward/record.url?scp=0031802262&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031802262&partnerID=8YFLogxK

U2 - 10.1016/S0025-5564(97)10015-3

DO - 10.1016/S0025-5564(97)10015-3

M3 - Article

C2 - 9610111

AN - SCOPUS:0031802262

VL - 149

SP - 57

EP - 76

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

IS - 1

ER -