Uncertainty Quantification of Random Microbial Growth in a Competitive Environment via Probability Density Functions

Bevia, Vicente José; Burgos Simón, Clara; Cortés, Juan Carlos; Villanueva Micó, Rafael J.

doi:10.3390/fractalfract5020026

Open AccessArticle

Uncertainty Quantification of Random Microbial Growth in a Competitive Environment via Probability Density Functions

by

Vicente José Bevia

,

Clara Burgos Simón

,

Juan Carlos Cortés

^*

and

Rafael J. Villanueva Micó

Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, 46022 Valencia, Spain

^*

Author to whom correspondence should be addressed.

Fractal Fract. 2021, 5(2), 26; https://doi.org/10.3390/fractalfract5020026

Submission received: 25 February 2021 / Revised: 19 March 2021 / Accepted: 20 March 2021 / Published: 24 March 2021

(This article belongs to the Special Issue Fractional Order Systems: Deterministic and Stochastic Analysis)

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Abstract

The Baranyi–Roberts model describes the dynamics of the volumetric densities of two interacting cell populations. We randomize this model by considering that the initial conditions are random variables whose distributions are determined by using sample data and the principle of maximum entropy. Subsequenly, we obtain the Liouville–Gibbs partial differential equation for the probability density function of the two-dimensional solution stochastic process. Because the exact solution of this equation is unaffordable, we use a finite volume scheme to numerically approximate the aforementioned probability density function. From this key information, we design an optimization procedure in order to determine the best growth rates of the Baranyi–Roberts model, so that the expectation of the numerical solution is as close as possible to the sample data. The results evidence good fitting that allows for performing reliable predictions.

Keywords: uncertainty quantification; competitive stochastic model; model simulation; model prediction; principle of maximum entropy; optimization

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MDPI and ACS Style

Bevia, V.J.; Burgos Simón, C.; Cortés, J.C.; Villanueva Micó, R.J. Uncertainty Quantification of Random Microbial Growth in a Competitive Environment via Probability Density Functions. Fractal Fract. 2021, 5, 26. https://doi.org/10.3390/fractalfract5020026

AMA Style

Bevia VJ, Burgos Simón C, Cortés JC, Villanueva Micó RJ. Uncertainty Quantification of Random Microbial Growth in a Competitive Environment via Probability Density Functions. Fractal and Fractional. 2021; 5(2):26. https://doi.org/10.3390/fractalfract5020026

Chicago/Turabian Style

Bevia, Vicente José, Clara Burgos Simón, Juan Carlos Cortés, and Rafael J. Villanueva Micó. 2021. "Uncertainty Quantification of Random Microbial Growth in a Competitive Environment via Probability Density Functions" Fractal and Fractional 5, no. 2: 26. https://doi.org/10.3390/fractalfract5020026

APA Style

Bevia, V. J., Burgos Simón, C., Cortés, J. C., & Villanueva Micó, R. J. (2021). Uncertainty Quantification of Random Microbial Growth in a Competitive Environment via Probability Density Functions. Fractal and Fractional, 5(2), 26. https://doi.org/10.3390/fractalfract5020026

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Uncertainty Quantification of Random Microbial Growth in a Competitive Environment via Probability Density Functions

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