The dynamics of bacteria-plasmid systems

Catherine A. Macken, Simon Asher Levin, Roland Waldstätter

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


We introduce a general model for the dynamics of a single plasmid type and a single bacterial cell type, following Stewart and Levin (1977) in subdividing the population into plasmid-bearing and plasmid-free cells. For the particular case of mortality being a linear function of population sizes, we demonstrate the existence of multiple stable states and threshold values, thus illustrating that, in some cases, the establishment of a population of plasmids may depend on introduction of plasmids at sufficiently high levels. We also analyze in detail, for a general monotonically increasing mortality function, the “epidemiological” case in which plasmids confer a net cost on their hosts, and demonstrate that it is possible for such plasmids to become established. Stewart and Levin previously demonstrated this effect in a more restricted model.

Original languageEnglish (US)
Pages (from-to)123-145
Number of pages23
JournalJournal of mathematical biology
Issue number2
StatePublished - Jan 1994

All Science Journal Classification (ASJC) codes

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


  • Coevolution
  • Plasmid dynamics
  • Population model


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