title: A size-structured model of bacterial growth and reproduction.
abstract: We consider a size-structured bacterial population model in which the rate of cell growth is both size- and time-dependent and the average per capita reproduction rate is specified as a model parameter. It is shown that the model admits classical solutions. The population-level and distribution-level behaviours of these solutions are then determined in terms of the model parameters. The distribution-level behaviour is found to be different from that found in similar models of bacterial population dynamics. Rather than convergence to a stable size distribution, we find that size distributions repeat in cycles. This phenomenon is observed in similar models only under special assumptions on the functional form of the size-dependent growth rate factor. Our main results are illustrated with examples, and we also provide an introductory study of the bacterial growth in a chemostat within the framework of our model.
authors.affiliation: Department of Mathematics and Statistics, Kennesaw State University, Kennesaw, GA 30144-5591, USA. sellerme@kennesaw.edu
authors.forename: S F
authors.initials: SF
authors.lastname: Ellermeyer
authors.forename: S S
authors.initials: SS
authors.lastname: Pilyugin
mesh_terms: D001419:Bacteria / Q000166:cytology* / Q000254:growth & development*; D008954:Models, Biological