Research article Special Issues

Mathematical model of interaction Escherichia coli and Coliphages


  • 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.

    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

    Related Papers:

    [1] Nick Cercone . What's the Big Deal About Big Data?. Big Data and Information Analytics, 2016, 1(1): 31-79. doi: 10.3934/bdia.2016.1.31
    [2] Ali Asgary, Jianhong Wu . ADERSIM-IBM partnership in big data. Big Data and Information Analytics, 2016, 1(4): 277-278. doi: 10.3934/bdia.2016010
    [3] Yaguang Huangfu, Guanqing Liang, Jiannong Cao . MatrixMap: Programming abstraction and implementation of matrix computation for big data analytics. Big Data and Information Analytics, 2016, 1(4): 349-376. doi: 10.3934/bdia.2016015
    [4] Pankaj Sharma, David Baglee, Jaime Campos, Erkki Jantunen . Big data collection and analysis for manufacturing organisations. Big Data and Information Analytics, 2017, 2(2): 127-139. doi: 10.3934/bdia.2017002
    [5] Enrico Capobianco . Born to be Big: data, graphs, and their entangled complexity. Big Data and Information Analytics, 2016, 1(2): 163-169. doi: 10.3934/bdia.2016002
    [6] John A. Doucette, Robin Cohen . A testbed to enable comparisons between competing approaches for computational social choice. Big Data and Information Analytics, 2016, 1(4): 309-340. doi: 10.3934/bdia.2016013
    [7] Hamzeh Khazaei, Marios Fokaefs, Saeed Zareian, Nasim Beigi-Mohammadi, Brian Ramprasad, Mark Shtern, Purwa Gaikwad, Marin Litoiu .
     How do I choose the right NoSQL solution? A comprehensive theoretical and experimental survey 
    . Big Data and Information Analytics, 2016, 1(2): 185-216. doi: 10.3934/bdia.2016004
    [8] Richard Boire . UNDERSTANDING AI IN A WORLD OF BIG DATA. Big Data and Information Analytics, 2018, 3(1): 22-42. doi: 10.3934/bdia.2018001
    [9] M Supriya, AJ Deepa . Machine learning approach on healthcare big data: a review. Big Data and Information Analytics, 2020, 5(1): 58-75. doi: 10.3934/bdia.2020005
    [10] Weidong Bao, Wenhua Xiao, Haoran Ji, Chao Chen, Xiaomin Zhu, Jianhong Wu . Towards big data processing in clouds: An online cost-minimization approach. Big Data and Information Analytics, 2016, 1(1): 15-29. doi: 10.3934/bdia.2016.1.15
  • 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.



    Researchers in the computational intelligence society have been consistently achieving progress in making machines more intelligent from various aspects, including representations, learning models, and optimization methods. The development of these techniques provides useful tools for big data and information analytics. This special issue aims at presenting recent advancements of combining computational intelligence methods with big data. We accepted 7 papers after a strict review process. Each paper was reviewed by at least two reviewers. We hope the accepted papers to this special issue will provide a useful reference for researchers who are interested in computational intelligence and big data, and inspire more possibilities of novel methods and applications.

    The accepted papers can be roughly divided into three categories, according to the aspects they involve.

    On the aspect of representation, the article "Multiple-instance learning for text categorization based on semantic representation" by Zhang et al. employs the multi-instance representation for text data. A text document is usually represented as a single feature vector, which could be insufficient to expose its rich content for learning. This paper, based on the popular word2vec technique, represents a document by multiple instances. In such a way, the semantic meanings of a document can be well exposed, and the experiments show improved performance over single instance representation.

    Another article "A comparative study of robustness measures for cancer signaling networks" by Zhou et al. studies the cancer signaling data represented as a network. The information exchange pathways in the cancer signaling network are essential to the cure of cancer, thus it is meaningful to find a sensitive measure of the network that is highly correlated with patient survivability. This work investigates the robustness of 14 typical cancer signaling networks. Experiments find out that the natural connectivity is a promising measurement, which could be expected to help cancer treatments.

    On the aspect of learning models, the extreme learning machine is a recently emerged simple neural network model with randomly determined connection weights. The article "Two-hidden-layer extreme learning machine based wrist vein recognition system" by Yue et al. employs such neural network with two hidden layers to achieve a good performance in the wrist vein recognition task with a satisfactory training time.

    Incremental ability of learning models are often appealing. The article "Selective further learning of hybrid ensemble for class imbalanced Increment learning" by Lin and Tang addresses the class imbalance issue which naturally arises in incremental learning, and proposes an ensemble-based method Selective Further Learning, where different component learners handle different issues of the learning. Experiments show that the proposed method outperforms some recent state-of-the-art approaches.

    On the aspect of optimization methods, the article "A clustering based mate selection for evolutionary optimization" by Zhang et al. introduces the mate selection mechanism into evolutionary algorithms. Helped by the clustering, the mate of an individual is restricted in the same cluster. With this new mechanism, the evolutionary algorithm optimizes a set of benchmark functions better.

    Optimization is also related with representation. In the article "A moving block sequence-based evolutionary algorithm for resource investment project scheduling problems" by Yuan et al. proposes the moving block sequence representation for the resource investment project scheduling problem. The new representation can guarantee some good properties of the solved solution, and consequently the proposed approach shows superior performance on 450 benchmark instances.

    Better optimization can lead to better learning. In the article "An evolutionary multiobjective method for low-rank and sparse matrix decomposition" by Wu et al, a multiobjective evolutionary approach is employed to solve the low-rank matrix decomposition problem. The multiobjective approach can well trade-off between low-rank and sparse objectives, leading to satisfied results on nature image analysis.

    We thank all the authors for their contributions to this special issue, and the reviewers for their careful and insightful reviews. We also thank Prof. Jianhong Wu and Prof. Zongben Xu, the Editor-in-Chiefs of the Big Data and Information Analytics journal, and Prof. Zhi-Hua Zhou from the Editorial Board of the journal for the full support of this special issue, and the Aimsciences staff for managing this special issue.




    [1] A. M. Comeau, G. F. Hatfull, H. M. Krisch, D. Lindell, N. H. Mann, D. Prangishvili, Exploring the prokaryotic virosphere, Res. Microbiol., 159 (2008), 306–313. https://doi.org/10.1016/j.resmic.2008.05.001 doi: 10.1016/j.resmic.2008.05.001
    [2] M. R. Clokie, A. D. Millard, A. V. Letarov, S. Heaphy, Phages in nature, Bacteriophage, 1 (2011), 31–45. https://doi.org/10.4161/bact.1.1.14942 doi: 10.4161/bact.1.1.14942
    [3] C. Howard-Varona, K. R. Hargreaves, S. T. Abedon, M. B. Sullivan, Lysogeny in nature: mechanisms, impact and ecology of temperate phages, ISME J., 11 (2017), 1511–1520. https://doi.org/10.1038/ismej.2017.16 doi: 10.1038/ismej.2017.16
    [4] J. R. Clark, J. B. March, Bacteriophages and biotechnology: vaccines, gene therapy and antibacterials, Trends Biotechnol., 24 (2006), 212–218. https://doi.org/10.1016/j.tibtech.2006.03.003 doi: 10.1016/j.tibtech.2006.03.003
    [5] I. U. Haq, W. N. Chaudhry, M. N. Akhtar, S. Andleeb, I. Qadri, Bacteriophages and their implications on future biotechnology: a review, Virol. J., 9 (2012), 1–8. https://doi.org/10.1186/1743-422X-9-9 doi: 10.1186/1743-422X-9-9
    [6] C. Loc-Carrillo, S. T. Abedon, Pros and cons of phage therapy, Bacteriophage, 1 (2011), 111–114. https://doi.org/10.4161/bact.1.2.14590 doi: 10.4161/bact.1.2.14590
    [7] R. Jain, A. L. Knorr, J. Bernacki, R. Srivastava, Investigation of bacteriophage MS2 viral dynamics using model discrimination analysis and the implications for phage therapy, Biotechnol. Progr., 22 (2006), 1650–1658. https://doi.org/10.1021/bp060161s doi: 10.1021/bp060161s
    [8] G. Beke, M. Stano, L. Klucar, Modelling the interaction between bacteriophages and their bacterial hosts, Math. Biosci., 279 (2016), 27–32. https://doi.org/10.1016/j.mbs.2016.06.009 doi: 10.1016/j.mbs.2016.06.009
    [9] B. J. Cairns, A. R. Timms, V. A. Jansen, I. F. Connerton, R. J. Payne, Quantitative models of in vitro bacteriophage–host dynamics and their application to phage therapy, PLoS Pathog., 5 (2009), e1000253. https://doi.org/10.1371/journal.ppat.1000253 doi: 10.1371/journal.ppat.1000253
    [10] H. Ndongmo Teytsa, B. Tsanou, S. Bowong, J. M. Lubuma, Bifurcation analysis of a phage-bacteria interaction model with prophage induction, Math. Med. Biol., 38 (2021), 28–58. https://doi.org/10.1093/imammb/dqaa010 doi: 10.1093/imammb/dqaa010
    [11] X. Li, R. Huang, M. He, Dynamics model analysis of bacteriophage infection of bacteria, Adv. Differ. Equations, 2021 (2021), 1–11. https://doi.org/10.1186/s13662-021-03466-x doi: 10.1186/s13662-021-03466-x
    [12] S. Pagliarini, A. Korobeinikov, A mathematical model of marine bacteriophage evolution, Roy. Soc. Open Sci., 5 (2018), 171661. https://doi.org/10.1098/rsos.171661 doi: 10.1098/rsos.171661
    [13] C. C. McCluskey, P. van den Driessche, Global analysis of two tuberculosis models, J. Dyn. Differ. Equations, 16 (2004), 139–166. https://doi.org/10.1023/B:JODY.0000041283.66784.3e doi: 10.1023/B:JODY.0000041283.66784.3e
    [14] M. Y. Li, J. S. Muldowney, On RA smith's autonomous convergence theorem, Rocky Mount. J. Math., 25 (1995), 365–379.
    [15] S. Marino, I. B. Hogue, C. J. Ray, D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theor. Biol., 254 (2008), 178–196. https://doi.org/10.1016/j.jtbi.2008.04.011 doi: 10.1016/j.jtbi.2008.04.011
    [16] M. Konopacki, B. Grygorcewicz, B. Dolegowska, M. Kordas, R. Rakoczy, Phagescore: A simple method for comparative evaluation of bacteriophages lytic activity, Biochem. Eng. J., 161 (2020), 107652. https://doi.org/10.1016/j.bej.2020.107652 doi: 10.1016/j.bej.2020.107652
    [17] M. C. Gómez, H. M. Yang, Mathematical model of the immune response to dengue virus, J. Appl. Math. Comput., 63 (2020), 455–478. https://doi.org/10.1007/s12190-020-01325-8 doi: 10.1007/s12190-020-01325-8
    [18] N. Principi, E. Silvestri, S. Esposito, Advantages and limitations of bacteriophages for the treatment of bacterial infections, Front. pharmacol., 10 (2019), 513. https://doi.org/10.3389/fphar.2019.00513 doi: 10.3389/fphar.2019.00513
    [19] M. Merabishvili, C. Vervaet, J. P. Pirnay, D. De Vos, G. Verbeken, J. Mast, et al., Stability of Staphylococcus aureus phage ISP after freeze-drying (lyophilization). PloS One, 8 (2013), e68797. https://doi.org/10.1371/journal.pone.0068797 doi: 10.1371/journal.pone.0068797
  • Reader Comments
  • © 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2995) PDF downloads(237) Cited by(0)

Article outline

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog