Biofilm Early Stages of Growth and Accumulation Theoretical Model

José Carvalho; Manuel Carrondo; Luis Bonilla

doi:10.20944/preprints202012.0673.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 24 December 2020 / Approved: 26 December 2020 / Online: 26 December 2020 (10:45:47 CET)
Version 2 : Received: 27 February 2021 / Approved: 1 March 2021 / Online: 1 March 2021 (13:13:47 CET)

A theoretical model to translate the evolution over time, in early stages, of growth and accumulation of biofilm bacterial mass is introduced. The model implies the solution of a system of differential-difference master equations. The application of an algorithm like Miller´s tree term recurrence, already known for Bessel functions of first kind, allows an exact calculation of the solutions of such equations, for a wide range of parameters values and time. For biofilm model a five term recurrence is deduced and applied in a backwards computation. A suitable normalisation condition completes the reach of the solution.

biofilm; Miller recurrent algorithm; Bessel functions; differential-difference master equations

Engineering, Automotive Engineering

Comment 1

Received: 1 March 2021
Commenter: José Carvalho
Commenter's Conflict of Interests: Author

Comment: New sections were included:
1. More detailed initial description of the model
2. A section of numerical examples
3. A conclusions section
4. A future work section

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Biofilm Early Stages of Growth and Accumulation Theoretical Model

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