Mean field mutation dynamics and the continuous Luria-Delbrück distribution

Eugene Kashdan, Lorenzo Pareschi
(14/12/2011 Mathematical Biosciences 240, (2012), pp. 223-230 arXiv:1112.2836)

The Luria-Delbrück mutation model has a long history and has been mathematically formulated in several different ways. Here we tackle the problem in the case of a continuous distribution using some mathematical tools from nonlinear statistical physics.

Starting from the classical formulations we derive the corresponding differential models and show that under a suitable mean field scaling they correspond to generalized Fokker-Planck equations for the mutants distribution whose solutions are given by the corresponding Luria-Delbrück distribution. Numerical results confirming the theoretical analysis are also presented.

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