Persistence of bacteria and phages in a chemostat

Hal Smith, Horst Thieme

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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
Issue number6
StatePublished - May 1 2012


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

ASJC Scopus subject areas

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


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