# American Institute of Mathematical Sciences

December  2013, 6(4): 1043-1055. doi: 10.3934/krm.2013.6.1043

## A kinetic description of mutation processes in bacteria

 1 University of Pavia, Department of Mathematics, Via Ferrata 1, 27100 Pavia

Received  September 2013 Revised  September 2013 Published  November 2013

The Luria--Delbrück mutation model has been mathematically formulated in a number of ways. Last, a mean field picture derived from a kinetic formulation has been derived by Kashdan and Pareschi in [18]. There, the Luria--Delbrück distribution appears as the solution of a Fokker-Planck like equation obtained as the quasi-invariant asymptotics of a linear Boltzmann equation for the number density of the number of mutated cells. This paper addresses the kinetic description for the Lea--Coulson formulation [21], as well as for the Kendall formulation [19], focusing on important modeling issues closely linked with the distribution of the number of mutants. The paper additionally emphasizes basic principles which not only help to unify existing results but also allow for a useful extensions.
Citation: Giuseppe Toscani. A kinetic description of mutation processes in bacteria. Kinetic & Related Models, 2013, 6 (4) : 1043-1055. doi: 10.3934/krm.2013.6.1043
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