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Stochastic modelling and control of antibiotic subtilin production

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Abstract

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.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Würzburg, Emil-Fischer-Strasse 30, 97074, Würzburg, Germany

    V. Thalhofer & A. Borzì

  2. Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II, 132 - 84084, Fisciano, Italy

    M. Annunziato

Authors
  1. V. Thalhofer
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  2. M. Annunziato
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  3. A. Borzì
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Corresponding author

Correspondence to M. Annunziato.

Additional information

Supported in part by the European Union under Grant Agreement Nr. 304617 ‘Multi-ITN STRIKE - Novel Methods in Computational Finance’ and by the Würzburg-Wrocław Center for Stochastic Computing.

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Thalhofer, V., Annunziato, M. & Borzì, A. Stochastic modelling and control of antibiotic subtilin production. J. Math. Biol. 73, 727–749 (2016). https://doi.org/10.1007/s00285-016-0968-6

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  • DOI: https://doi.org/10.1007/s00285-016-0968-6

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