A kinetic description of mutation processes in bacteria

The Luria--Delbrück mutation model has beenmathematically formulated in a number of ways. Last, a mean fieldpicture derived from a kinetic formulation has been derived byKashdan and Pareschi in 18. There, the Luria--Delbrückdistribution appears as the solution of a Fokker-Planck likeequation obtained as the quasi-invariant asymptotics of a linearBoltzmann equation for the number density of the number of mutatedcells. This paper addresses the kinetic description for theLea--Coulson formulation 21, as well as for the Kendallformulation 19, focusing on important modeling issuesclosely linked with the distribution of the number of mutants. Thepaper additionally emphasizes basic principles which not only helpto unify existing results but also allow for a useful extensions.