Mathematical model of interaction <i>Escherichia coli</i> and Coliphages

Miller Cerón Gómez; Eduardo Ibarguen Mondragon; Eddy Lopez Molano; Arsenio Hidalgo-Troya; Maria A. Mármol-Martínez; Deisy Lorena Guerrero-Ceballos; Mario A. Pantoja; Camilo Paz-García; Jenny Gómez-Arrieta; Mariela Burbano-Rosero; Miller Cerón Gómez; Eduardo Ibarguen Mondragon; Eddy Lopez Molano; Arsenio Hidalgo-Troya; Maria A. Mármol-Martínez; Deisy Lorena Guerrero-Ceballos; Mario A. Pantoja; Camilo Paz-García; Jenny Gómez-Arrieta; Mariela Burbano-Rosero

doi:10.3934/mbe.2023426

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 6: 9712-9727. doi: 10.3934/mbe.2023426

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Mathematical model of interaction Escherichia coli and Coliphages

1.
Department of Mathematics, University of Narño, Pasto, Clle 18 - Cra 50, Colombia
2.
Department of Biology, University of Narño, Pasto, Clle 18 - Cra 50, Colombia

Academic Editor: Xiang-Sheng Wang

Received: 24 August 2022 Revised: 21 November 2022 Accepted: 05 December 2022 Published: 23 March 2023

We propose a mathematical model based in ordinary differential equations between bacterial pathogen and Bacteriophages to describe the infection dynamics of these populations, for which we use a nonlinear function with an inhibitory effect. We study the stability of the model using the Lyapunov theory and the second additive compound matrix and perform a global sensitivity analysis to elucidate the most influential parameters in the model, besides we make a parameter estimation using growth data of Escherichia coli (E.coli) bacteria in presence of Coliphages (bacteriophages that infect E.coli) with different multiplicity of infection. We found a threshold that indicates whether the bacteriophage concentration will coexist with the bacterium (the coexistence equilibrium) or become extinct (phages extinction equilibrium), the first equilibrium is locally asymptotically stable while the other is globally asymptotically stable depending on the magnitude of this threshold. Beside we found that the dynamics of the model is particularly affected by infection rate of bacteria and Half-saturation phages density. Parameter estimation show that all multiplicities of infection are effective in eliminating infected bacteria but the smaller one leaves a higher number of bacteriophages at the end of this elimination.
- coliphages,
- E.coli,
- phage-bacteria,
- Lyapunov method,
- population dynamics
Citation: Miller Cerón Gómez, Eduardo Ibarguen Mondragon, Eddy Lopez Molano, Arsenio Hidalgo-Troya, Maria A. Mármol-Martínez, Deisy Lorena Guerrero-Ceballos, Mario A. Pantoja, Camilo Paz-García, Jenny Gómez-Arrieta, Mariela Burbano-Rosero. Mathematical model of interaction Escherichia coli and Coliphages[J]. Mathematical Biosciences and Engineering, 2023, 20(6): 9712-9727. doi: 10.3934/mbe.2023426

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Abstract

We propose a mathematical model based in ordinary differential equations between bacterial pathogen and Bacteriophages to describe the infection dynamics of these populations, for which we use a nonlinear function with an inhibitory effect. We study the stability of the model using the Lyapunov theory and the second additive compound matrix and perform a global sensitivity analysis to elucidate the most influential parameters in the model, besides we make a parameter estimation using growth data of Escherichia coli (E.coli) bacteria in presence of Coliphages (bacteriophages that infect E.coli) with different multiplicity of infection. We found a threshold that indicates whether the bacteriophage concentration will coexist with the bacterium (the coexistence equilibrium) or become extinct (phages extinction equilibrium), the first equilibrium is locally asymptotically stable while the other is globally asymptotically stable depending on the magnitude of this threshold. Beside we found that the dynamics of the model is particularly affected by infection rate of bacteria and Half-saturation phages density. Parameter estimation show that all multiplicities of infection are effective in eliminating infected bacteria but the smaller one leaves a higher number of bacteriophages at the end of this elimination.

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