A size-structured model of bacterial growth and reproduction |
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Authors: | S F Ellermeyer S S Pilyugin |
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Institution: | a Department of Mathematics and Statistics , Kennesaw State University , Kennesaw , GA , 30144-5591 , USA. |
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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. |
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