Mathematical modeling to evaluate potato cultivation in high-andean soils using data analysis and the Runge Kutta method

Authors

  • Irla Mantilla Núñez Facultad de Ciencias, Universidad Nacional de Ingeniería. Perú.
  • Juan Reymundo P. Facultad de Ciencias, Universidad Nacional de Ingeniería. Perú.

DOI:

https://doi.org/10.17268/sel.mat.2024.01.06

Keywords:

Rancha fungus, environmental risk in potato crop, data cleaning, data analysis, Lotka- Volterra model, Runge-Kutta

Abstract

According to data collected by the International Potato Center (CIP) and the Departmental Federation of Peasant Communities (FEDECH), regarding the Huancavelica region. One of the most devastating diseases in the potato crop is ”Rancha”; scientifically known as Phytophtora infestan. Frog can be controlled by the application of fungicides, but due to the excessive growth of the population density of this pathogen produced by the frog fungus, it would be necessary to apply more fungicides, which poses a high environmental and  human health risk to those who consume this type of tuber in their diet. To measure the population growth of both species, a database will be built related to the percentage of potato crops per hectare that are attacked by this type of fungus. In this sense, a numerical mathematical model will be developed based on the Lotka-Volterra type differential equation system, which is solved with the Runge-Kutta RK2 and RK4 method, in order to contribute, in a non-invasive way, with an alternative for the prevention and control of this disease in potato crops in high Andean soils.

References

Mafra-Neto A, Wright M, Fettig C, Progar R, Munson S, Blackford D, et al. CHAPTER 15 - Repellent semiochemical solutions to mitigate the impacts of global climate change on arthropod pests. In: Corona C, Debboun M, Coats J, editors. Advances in Arthropod Repellents. Academic Press; 2022. p. 279-322. Available from: https://doi.org/10.1016/B978-0-323-85411-5.00010-8.

Vargas OR. Crisis alimentaria mundial y sus repercusiones en Nicaragua. Madrid, España Serie Avances de Investigación. 2010;(38):1885-913.

Ripa R, Larral P, et al. Manejo de plagas en paltos y cítricos. Colección Libros INIA-Instituto de Investigaciones Agropecuarias. 2008:42-56.

Evans CM, Findley G. Analytic solutions to the Lotka-Volterra model for sustained chemical oscillations.1998.

May-Cen IdJ. Modelos de dinámica poblacional en ecología. Revista del Centro de Graduados e Investigación. Instituto Tecnológico de Mérida. 2016;32(60):50-5.

Stef de Haan ARC Ana Taipe Palomino. Catálogo de variedades de papa nativa de Huancavelica-Perú. International Potato Center(CIP). 2006. "[Online; accessed 22 abril 2022]". Available from: https://cipotato.org/wp-content/uploads/PDF/003524.pdf.

Luis R. Estadística descriptiva. Las Prensas de Ciencias, Facultad de Ciencias, UNAM, 2017;

Available from: ’https://lya.fciencias.unam.mx/lars/Publicaciones/ed2017.pdf’.

Baigent S. Lotka-Volterra Dynamics-An Introduction.[Online] Available at:http://www.ltcc. ac. uk/courses/BioMathematics. LTCC LV2010 [Accessed 16 5 2022]. 2010.

Cano Cancela A. Sistemas de Lotka-Volterra en din´amica poblacional. 2011.

Bruce P, Bruce A, Gedeck P. Estadística práctica para ciencia de datos con R y Python. Marcombo; 2022.

VanderPlas J. Python data science handbook: Essential tools for working with data.Reilly Media, Inc.;2016.

Tukey JW, et al. Exploratory data analysis. vol. 2. Reading, MA; 1977.

Juan Antonio CV. Introducción al Machine Learning. 2022:9-15. Available from: https://github.com/gcoronelc/CTIC-CIENCIA-DE-DATOS-MOD-01-2022A.

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Published

2024-07-29

How to Cite

Mantilla Núñez, I., & Reymundo P., J. . (2024). Mathematical modeling to evaluate potato cultivation in high-andean soils using data analysis and the Runge Kutta method. Selecciones Matemáticas, 11(01), 69 - 87. https://doi.org/10.17268/sel.mat.2024.01.06

Issue

Vol. 11 No. 01 (2024): January - July

Section

Articles

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