Stochastic modelling and control of antibiotic subtilin production

A stochastic hybrid model for the production of the antibiotic subtilin by the Bacillus subtilis is investigated. This model consists of 5 variables with four possible discrete dynamical states and this high dimensionality represents a bottleneck for using statistical tools that require to solve the corresponding Fokker-Planck problem. For this reason, a suitable reduced model with 3 variables and two dynamical states is proposed. The corresponding Fokker-Planck hyperbolic system is used to validate the evolution statistics and to construct a robust feedback control strategy to increase subtilin production. Results of numerical experiments are presented that show the effectiveness of the proposed control scheme.