Lag time in microbe growth as an age-dependent branching process with two phase types |
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Authors: | Mark J Christensen R Shonkwiler |
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Institution: | (1) School of Mathematics, Georgia Institute of Technology, 30332 Atlanta, Georgia, USA |
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Abstract: | We study a two-type, age-dependent branching process in which the branching probabilities of one of the types may vary with
time. Specifically this modification of the Bellman-Harris process starts with a Type I particle which may either die or change
to a Type II particle depending upon a time varying probability. A Type II particle may either die or reproduce with fixed
probabilities but may not return to a particle of Type I. In this way the process models the lag phenomenon observed in microbe
growth subsequent to transfer to a new culture medium while the organism is adapting to its new environment.
We show that if the mean reproduction rate of Type II particles exceeds 1, then the population size grows exponentially. Further
the extinction probability for this process is related to that of the Bellman-Harris process. Finally the governing equations
are solved for several choices of the growth parameters and the solutions are graphically displayed showing that a wide variety
of behavior can be modeled by this process. |
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Keywords: | |
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