Geodesic
Mathematical model “consumer — resource’’ on a liner range and its application for modeling the spread of late blight of potato
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 18 (2022) no. 4, pp. 548-554 Cet article a éte moissonné depuis la source Math-Net.Ru

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A model of consumer distribution on a fixed resource, which is uniformly distributed through a linear area, is presented. The model is based on the Cauchy problem for a system of partial differential equations. The stability of the system is studied. The physical basis of the model is the spread of late blight over the territory of a trophic resource. A qualitative picture of the process under consideration coincides with field data obtained as a result of modeling. The model describes "consumer’’ development not even at the moment, but through linear range. Thus assesment of damaged field square is possible.
Keywords: mathematical model of late blight development, late blight, mathematical model of phytopathology, linear range. 
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     author = {N. A. Gasratova},
     title = {Mathematical model {\textquotedblleft}consumer {\textemdash} resource{\textquoteright}{\textquoteright} on a liner range and its application for modeling the spread of late blight of potato},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {548--554},
     year = {2022},
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N. A. Gasratova. Mathematical model “consumer — resource’’ on a liner range and its application for modeling the spread of late blight of potato. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 18 (2022) no. 4, pp. 548-554. http://geodesic.mathdoc.fr/item/VSPUI_2022_18_4_a8/

[1] Narouei-Khandan H. A., Shakya S. K., Garrett K. A., Goss E. M., Dufault N. S., Andrade-Piedra J. L., Asseng S., Wallach D., van Bruggen A. H. C., “BLIGHTSIM: A new potato late blight model simulating the response of Phytophthora infestans to diurnal temperature and humidity fluctuations in relation to climate change”, Pathogens, 9:8 (2020), 659–679 | DOI

[2] Firester B., Shtienberg D., Blank L., “Modelling the spatiotemporal dynamics of Phytophthora infestans at a regional scale”, Plant Pathology, 67 (2018), 1552–1561 | DOI

[3] Riznichenko G. Yu., Mathematical methods in biology and ecology. Biophysical dynamics of production processes, In 2 pt., v. 1, Textbook for universities, 3$^{\rm rd}$ ed., revised and additional, Yurayt Publ., M., 2020, 210 pp. (In Russian)

[4] Owolabi K. M., “Mathematical study of two-variable systems with adaptive numerical methods”, Siberian Journal of Calculating Mathematics, 19:3 (2016), 281–295 (In Russian) | DOI | MR

[5] Filippov A. V., “Potato late blight”, Defence and quarantine of plans, 2012, no. 5, suppl., 61–87 (In Russian)

[6] Chikin Yu. A., General phytopathology, v. 1, Textbook, Tomsk State University Press, Tomsk, 2001, 170 pp. (In Russian)

[7] Skelsey P., Rossing W. A. H., Kessel G. J. T., van der Werf W., “Invasion of Phytophthora infestans at the landscape level: How do spatial scale and weather modulate the consequences of spatial heterogeneity in host resistance?”, Phytopathology, 100:11 (2010), 1146–1161 | DOI

[8] Fry W. E., Grünwald N. J., “Introduction to Oomycetes”, The Plant Health Instructor, 2010 | DOI

[9] Leifert C., Wilcockson S. J., Blight-MOP: Development of a systems approach for the management of late blight (caused by Phytophthora infestans) in EU organic potato production, University of Newcastle, Newcastle, UK, 2005 (accessed: June 10, 2022) | MR

[10] Andrade-Piedra J. L., Hijmans R. J., Juárez H. S., Forbes G. A., Shtienberg D., Fry W. E., “Simulation of potato late blight in the Andes. II: Validation of the late blight model”, Phytopathology, 95:10 (2005), 1200–1208 | DOI