Journal of Mathematical Biology

, Volume 73, Issue 3, pp 727–749 | Cite as

Stochastic modelling and control of antibiotic subtilin production

  • V. Thalhofer
  • M. AnnunziatoEmail author
  • A. Borzì


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.


Subtilin antibiotic Optimal control antibiotic production Stochastic hybrid biology modelling 

Mathematics Subject Classification

35L45 35Q92 60J25 60K20 49L20 49K20 65M06 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institut für MathematikUniversität WürzburgWürzburgGermany
  2. 2.Dipartimento di MatematicaUniversità degli Studi di SalernoFiscianoItaly

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