Persistence of bacteria and phages in a chemostat

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

The model of bacteriophage predation on bacteria in a chemostat formulated by Levin et al. (Am Nat 111:3-24, 1977) is generalized to include a distributed latent period, distributed viral progeny release from infected bacteria, unproductive adsorption of phages to infected cells, and possible nutrient uptake by infected cells. Indeed, two formulations of the model are given: a system of delay differential equations with infinite delay, and a more general infection-age model that leads to a system of integro-differential equations. It is shown that the bacteria persist, and sharp conditions for persistence and extinction of phages are determined by the reproductive ratio for phage relative to the phage-free equilibrium. A novel feature of our analysis is the use of the Laplace transform.

Original languageEnglish (US)
Pages (from-to)951-979
Number of pages29
JournalJournal of Mathematical Biology
Volume64
Issue number6
DOIs
StatePublished - May 2012

Fingerprint

Chemostats
Chemostat
Bacteriophages
bacteriophages
Bacteria
Persistence
bacteria
Infinite Delay
Cell
Delay Differential Equations
Nutrients
Adsorption
Integro-differential Equation
Extinction
Laplace transform
Infection
latent period
Model
Integrodifferential equations
Laplace transforms

Keywords

  • Delay differential equations
  • Infection-age model
  • Laplace transform
  • Persistence
  • Phage

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics
  • Modeling and Simulation

Cite this

Persistence of bacteria and phages in a chemostat. / Smith, Hal; Thieme, Horst.

In: Journal of Mathematical Biology, Vol. 64, No. 6, 05.2012, p. 951-979.

Research output: Contribution to journalArticle

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