A model of prey bacteria,predator bacteria,and bacteriophage in continuous culture

Mathematical models are presented for one-, two- and three -trophic-level microbial systems in continuous culture, based on the respective interactions of Escherichia coli and limiting glucose; glucose, E. coli, and the predaceous bacterium Bdellovibrio bacteriovorus; and glucose, E. coli, B. bacteriovorus, and a virus parasitic on B. bacteriovorus. These models contain explicit time lags to represent reproductive latent periods, and the importance of these to the behavior of the models is demonstrated. The models' behavior was investigated by algebraic analysis and by computer simulation using literature values for the parameters in the equations; equilibrium conditions and stability properties for the various microbial systems are presented over a wide range of potential environmental conditions. A sensitivity analysis indicates which parameters must be most accurately known in order to validate the model experimentally. The results delineate the range of experimental conditions permitting the study of all these continuous culture systems in the laboratory and generate predictions about persistence of such multi-level microbial systems in natures