Abstract
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 language | English (US) |
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Pages (from-to) | 123-145 |
Number of pages | 23 |
Journal | Journal of mathematical biology |
Volume | 32 |
Issue number | 2 |
DOIs | |
State | Published - Jan 1994 |
All Science Journal Classification (ASJC) codes
- Modeling and Simulation
- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics
Keywords
- Coevolution
- Plasmid dynamics
- Population model