Nonlinear age-dependent population dynamics in continuously propagated bacterial cultures

Abstract Using results and techniques from the theory of Volterra integral equations, we investigate the existence, uniqueness, positivity, and boundedness of solutions, the existence of equilibrium solutions, and the stability of equilibria of a nonlinear age-dependent model for bacterial growth in a continuous fermentation process. The demographic parameters of the model, such as the growth, death, and fission rates of the cells, depend (in a nonlinear way) on the substrate concentration in the reactor tank.