Modeling and numerical simulation of E. coli dynamics in water body

Modeling and numerical simulation of E. coli dynamics in water body

Authors

DOI:

https://doi.org/10.5433/1679-0375.2022v43n1Espp41

Keywords:

Mathematical modeling, contamination bioindicators, environmental monitoring

Abstract

This article discusses the importance of monitoring water quality in public health and use of mathematical modeling to predict environmental impact. For monitoring, the E. coli indicator was chosen, and a one-dimensional hydrodynamic equation was used for mathematical simulation, which was solved using the Crank-Nilcolson method. The results of the mathematical model and developed algorithm were validated according to data from the literature.

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Author Biographies

Dennis da Silva Ferreira, Federal University of São Carlos - UFSCar

PhD student, Dept. Chemistry, UFSCar, SP

Warlyton Silva Martins, Federal University of Tocantins - UFT

PhD student, Depto. Plant Production, UFT, Gurupi, TO,

Grasiele Soares Cavallini, Federal University of Tocantins - UFT

Prof. Dr., Depto. Chemistry and Plant Production, UFT, Gurupi, TO

Douglas Azevedo Castro, Federal University of Tocantins - UFT

Prof. Dr., Depto. Chemistry, UFT, Gurupi, TO, Brazil

References

ARBOS, K. A. et al. Qualidade microbiológica da água para consumo humano no loteamento Nova Esperança: Litoral Sul da Paraíba e sua importância para a Saúde Pública. Revista de Ciências da Saúde Nova Esperança, Gramame, v. 15, n. 2, p. 50-56, 2017. DOI: https://doi.org/10.17695/revcsnevol15n2p50-56. DOI: https://doi.org/10.17695/issn.2317-7160.v15n2a2017p50-56

BALDOCHI, M. A. Utilização do modelo QUAL2E como apoio ao gerenciamento da qualidade das águas da bacia do córrego dos Bagres. 2002. Dissertation (Master's) - Universidade de São Paulo, São Paulo, 2002.

BASSANEZI, R. Ensino-aprendizagem com Modelagem matemática. São Paulo: Contexto, 2002.

BRANDT, A. Multi-level adaptive solutions to boundary- value problems. Mathematics of Computation, Providence, v. 31, p. 333-390, 1977. DOI:https://doi.org/10.2307/2006422. DOI: https://doi.org/10.1090/S0025-5718-1977-0431719-X

CASTRO, D. A.; GOMES, S. M.; STOLFI, J. An adaptive multiresolution method on dyadic grids: application to transport equations. Journal of Computational and Applied Mathematics, Antwerpen, v. 236, n. 15, p. 3636-3646, 2012. DOI: https://doi.org/10.1016/j.cam.2011.05.044. DOI: https://doi.org/10.1016/j.cam.2011.05.044

CASTRO, D. A.; GOMES, S. M.; STOLFI, J. High-order adaptive finite-volume schemes in the context of multiresolution analysis for dyadic grids. Computational and Applied Mathematics, Petrópolis, v. 35, p. 1-16, 2016. DOI: https://doi.org/10.1007/s40314-014-0159-2. DOI: https://doi.org/10.1007/s40314-014-0159-2

CLILVERD , H. M.; THOMPSON, J. R.; HEPPELL, C. M.; SAYER, C. D.; AXMACHER, J. C. Coupled hydrological/hydraulic modelling of river restoration impacts and floodplain hydrodynamics. River Research and Applications, Chichester, v. 32, n. 9, p. 1927-1948, 2016. DOI: https://doi.org/10.1002/rra.3036. DOI: https://doi.org/10.1002/rra.3036

COURANT, R;. FRIEDRICHS, K.; LEWY, H. On the partial difference equations of mathematical physics. IBM Journal, Armonk, v. 11, n. 2, p. 215-234, 1967. DOI: https://doi.org/10.1147/rd.112.0215

CRANK, J.; NICOLSON, P. A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge, v. 43, n. 1, p. 50-67, 1947. DOI: https://doi.org/10.1017/S0305004100023197. DOI: https://doi.org/10.1017/S0305004100023197

DIAS, N. Obtenção de uma solução analítica da equação de difusão-advecção com decaimento de 1a ordem pelo método da transformação de similaridade generalizada. Revista Brasileira de Recursos Hídricos, Porto Alegre, v.8, p. 181-188, 2003 DOI: https://doi.org/10.21168/rbrh.v8n1.p181-188

GALDINO, A. A técnica do super-passo na resolução numérica de equações diferenciais parciais parabólicas. 2006. Thesis (Doctor) - Universidade de São Paulo, São Paulo, 2006.

JOBIM, G. S. Dispersão de poluentes: simulação numérica do Lago Guaíba. 2012. Dissertation (Master's) - Universidade Federal do Rio Grande do Sul, Porto Alegre, 2012.

LEVEQUE, R. J. Finite volume methods for hyperbolic problems. Cambridge: Cambridge University Press, 2002. (Cambridge texts in Applied Mathematics). DOI: https://doi.org/10.1017/CBO9780511791253. DOI: https://doi.org/10.1017/CBO9780511791253

LIU, W.-C.; CHAN, W.-T.; YOUNG, C.-C. Modeling fecal coliform contamination in a tidal Danshuei River estuarine system. Science of The Total Environment, Amsterdam, v. 502, p. 632-640, 2015. DOI: https://doi.org/10.1016/j.scitotenv.2014.09.065. DOI: https://doi.org/10.1016/j.scitotenv.2014.09.065

OLIVEIRA, R. E. Dispersão de contaminantes em rios e canais através do método GILTT. 2015. Dissertation (Master's) - Universidade Federal de Pelotas, Pelotas, 2015.

OSINSKA, A.; KORZENIEWSKA, E.; HARNISZ, M.; NIESTEPSKI, S. The prevalence and characterization of antibiotic-resistant and virulent Escherichia coli strains in the municipal wastewater system and their environmental fate. Science of The Total Environment, Amsterdam, v. 577, p. 367-375, 2016. DOI: https://doi.org/10.1016/j.scitotenv.2016.10.203 DOI: https://doi.org/10.1016/j.scitotenv.2016.10.203

SCILAB 6.1.1. Rungis: Scilab, 2021. 1 software. Available from: https://www.scilab.org/. Acess: July 25, 2021.

SEFFRIN, G. F. F. Simulação atual e previsão futura da qualidade das águas do rio Ibicuí utilizando o modelo QUAL2E. 2001. Thesis (Doctor) - Universidade Federal de Santa Maria, Santa Maria, 2001.

SOCOLOFSKY, S. A.; JIRKA, G. H. Environmental fluid mechanics. part I: mass transfer and diffusion. 2nd ed. Karlsruh: Institut fur Hydromechanik, 2002. (Engineering-lectures). Available from: https://publikationen.bibliothek.kit.edu/1542004. Acess: Jully 25, 2021.

TUNDISI, J. G. Recursos hídricos no futuro: problemas e soluções. Estudos Avançados, São Paulo, v. 22, p. 7-16, 2008. DOI: https://doi.org/10.1590/S0103-40142008000200002

VON NEUMANN, J. A letter to V. Bush. In: REDEI, M. (ed.). John von Neumann: selected letters. London: American Mathematical Society, 1949. p. 103-111. (History of Mathematics, v. 27).

WESSELING, P. An introduction to multigrid methods. Philadelphia: R.T. Edwards, 2004.

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Published

2022-11-21

How to Cite

Ferreira, D. da S., Martins, W. S., Cavallini, G. S., & Castro, D. A. (2022). Modeling and numerical simulation of E. coli dynamics in water body. Semina: Ciências Exatas E Tecnológicas, 43(1Esp), 41–50. https://doi.org/10.5433/1679-0375.2022v43n1Espp41

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