A mathematical model of flavescence dorée in grapevines by considering seasonality

Fernando Huancas; Aníbal Coronel; Rodolfo Vidal; Stefan Berres; Humberto Brito; Fernando Huancas; Aníbal Coronel; Rodolfo Vidal; Stefan Berres; Humberto Brito

doi:10.3934/mbe.2024332

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 11: 7554-7581. doi: 10.3934/mbe.2024332

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A mathematical model of flavescence dorée in grapevines by considering seasonality

1.
Departamento de Matemática, Facultad de Ciencias Naturales, Matemáticas y del Medio Ambiente, Universidad Tecnológica Metropolitana, Las Palmeras No. 3360, Ññoa-Santiago 7750000, Chile
2.
GMA, Departamento de Ciencias Básicas-Centro de Ciencias Exactas CCE-UBB, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Chillán 3780000, Chile
3.
Núcleo de Investigación en Bioproductos y Materiales Avanzados (BioMA), Universidad Católica de Temuco, Temuco 4780002, Chile
4.
Integrata-Stiftung für humane Nutzung der Informationstechnologie, Vor dem Kreuzberg 28, 72070 Tübingen, Deutschland

Received: 05 August 2024 Revised: 10 October 2024 Accepted: 04 November 2024 Published: 13 November 2024

This paper presents a mathematical model to describe the spread of flavescence dorée, a disease caused by the bacterium Candidatus Phytoplasma vitis, which is transmitted by the insect vector Scaphoideus titanus in grapevine crops. The key contribution of this work is the derivation of conditions under which positive periodic solutions exist. These conditions are based on the assumption that key factors such as recruitment rates, disease transmission, and vector infectivity vary periodically, thus reflecting seasonal changes. The existence of these periodic solutions is proven using the degree theory, and numerical examples are provided to support the theoretical findings. This model aims to enhance the understanding of the epidemiological dynamics of flavescence dorée and contribute to developing better control strategies to manage the disease in grapevines.
Citation: Fernando Huancas, Aníbal Coronel, Rodolfo Vidal, Stefan Berres, Humberto Brito. A mathematical model of flavescence dorée in grapevines by considering seasonality[J]. Mathematical Biosciences and Engineering, 2024, 21(11): 7554-7581. doi: 10.3934/mbe.2024332

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Abstract

This paper presents a mathematical model to describe the spread of flavescence dorée, a disease caused by the bacterium Candidatus Phytoplasma vitis, which is transmitted by the insect vector Scaphoideus titanus in grapevine crops. The key contribution of this work is the derivation of conditions under which positive periodic solutions exist. These conditions are based on the assumption that key factors such as recruitment rates, disease transmission, and vector infectivity vary periodically, thus reflecting seasonal changes. The existence of these periodic solutions is proven using the degree theory, and numerical examples are provided to support the theoretical findings. This model aims to enhance the understanding of the epidemiological dynamics of flavescence dorée and contribute to developing better control strategies to manage the disease in grapevines.

References

[1]	H. González, Specialization on a global scale and agrifood vulnerability: 30 years of export agriculture in Mexico, Dev. Stud. Res., 1 (2014), 295–310. https://doi.org/10.1080/21665095.2014.929973 doi: 10.1080/21665095.2014.929973
[2]	A. M. Buainain, M. R. Sousa, Z. Navarro, Globalization and Agriculture: Redefining Unequal Development, Lexington Books, USA, 2017.
[3]	D. R. Krichker, O. A. Ruschitskaya, The formation and development of priority exports of organic products of agro-industrial complex of the urals region, AIP Conf. Proc., 2921 (2023), 090006. https://doi.org/10.1063/5.0164569 doi: 10.1063/5.0164569
[4]	K. Anderson, The World's Wine Markets: Globalization at Work, Edward Elgar Publishing, UK, 2004. https://doi.org/10.4337/9781845420765.00001
[5]	G. Campbell, N. Guibert, Wine, Society, and Globalization: Multidisciplinary Perspectives on the Wine Industry, Palgrave Macmillan, NY, 2007. https://doi.org/10.1057/9780230609907
[6]	M. Berns, A.Townend, Z. Khayat, B. Balagopal, M. Reeves, M. S. Hopkins, et al., Sustainability and competitive advantage, Sloan Manage. Rev., 51 (2009), 19–26.
[7]	J. Carrillo-Hemosilla, P. del Rio, T. Könnölä, Diversity of eco-innovations: reflections from selected case studies, J. Cleaner Prod., 18 (2010), 1073–1083. https://doi.org/10.1016/j.jclepro.2010.02.014 doi: 10.1016/j.jclepro.2010.02.014
[8]	A. Gilinsky, S. K. Newtona, R. F. Vega, Sustainability in the global wine industry: concepts and cases, Agric. Agric. Sci. Procedia, 8 (2016), 37–49. https://doi.org/10.1016/j.aaspro.2016.02.006 doi: 10.1016/j.aaspro.2016.02.006
[9]	E. Fleming, S. Mounter, B. Grant, G. Griffith, R. Villano, The new world challenge: Performance trends in wine production in major wine-exporting countries in the 2000s and their implications for the Australian wine industry, Wine Econ. Policy, 3 (2014), 115–126. https://doi.org/10.1016/j.wep.2014.12.002 doi: 10.1016/j.wep.2014.12.002
[10]	J. M. Núñez, A. Espejo, F. J. Fuentes, New scenario for the Spanish wine sector, International strategic perspectives, (in Spanish) Boletín económico de ICE, 3068 (2015), 57–67. https://doi.org/10.32796/bice.2015.3068.5512
[11]	F. Lessio, A. Portaluri, F. Paparella, A. Alma, A mathematical model of flavescence dorée epidemiology, Ecol. Modell., 312 (2015), 41–53. https://doi.org/10.1016/j.ecolmodel.2015.05.014 doi: 10.1016/j.ecolmodel.2015.05.014
[12]	F. Lessio, A. Alma, Models applied to grapevine pests: A review, Insects, 12 (2021), 169. https://doi.org/10.3390/insects12020169 doi: 10.3390/insects12020169
[13]	A. Alma, F. Lessio, H. Nickel, Insects as phytoplasma vectors: Ecological and epidemiological aspects, in Phytoplasmas: Plant Pathogenic Bacteria - II, Springer, Singapore, (2019), 1–25. https://doi.org/10.1007/978-981-13-2832-9_1
[14]	G. Daglio, Potential field detection of flavescence dorée and esca diseases using a ground sensing optical system, Biosyst. Eng., 215 (2022), 203–214. https://doi.org/10.1016/j.biosystemseng.2022.01.009 doi: 10.1016/j.biosystemseng.2022.01.009
[15]	F. Tacoli, N. Mori, A. Pozzebon, E. Cargnus, S. Da Viá, P. Zandigiacomo, et al., Control of scaphoideus titanus with natural products in organic vineyards, Insects, 8 (2017), 129. https://doi.org/10.3390/insects8040129 doi: 10.3390/insects8040129
[16]	J. Kranz, Epidemics of Plant Diseases Mathematical Analysis and Modeling, Springer Berlin, Heidelberg, 2004. https://doi.org/10.1007/978-3-642-75398-5
[17]	F. Brauer, C. Castillo-Chavez, Z. Feng, Mathematical Models in Epidemiology, Springer New York, NY, 2019. https://doi.org/10.1007/978-1-4939-9828-9
[18]	H. Fang, M. Wang, T. Zhou, Existence of positive periodic solution of a hepatitis B virus infection model, Math. Methods Appl. Sci., 38 (2015), 188–196. https://doi.org/10.1002/mma.3074 doi: 10.1002/mma.3074
[19]	J. Lourenço, M. Maia de Lima, N. R. Faria, A. Walker, U. MOritz, C. J. Villabona-Arenas, et al., Epidemiological and ecological determinants of Zika virus transmission in an urban setting, eLife, 6 (2017), e29820. https://doi.org/10.7554/eLife.29820 doi: 10.7554/eLife.29820
[20]	R. Ranjan, Predictions for COVID-19 outbreak in India using epidemiological models, MedRxiv, 2020 (2020), 11. https://doi.org/10.1101/2020.04.02.20051466 doi: 10.1101/2020.04.02.20051466
[21]	M. Martcheva, An Introduction to Mathematical Epidemiology, Springer New York, NY, 2015. https://doi.org/10.1007/978-1-4899-7612-3
[22]	T. Smith, G. F. Killeen, N. Maire, A. Ross, L. Molineaux, F. Tediosi, et al., Mathematical modeling of the impact of malaria vaccines on the clinical epidemiology and natural history of Plasmodium falciparum malaria: Overview, Am. J. Trop. Med. Hyg., 75 (2010), 1–10. https://doi.org/10.4269/ajtmh.2006.75.2_suppl.0750001 doi: 10.4269/ajtmh.2006.75.2_suppl.0750001
[23]	W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc. London Ser. A Math. Phys. Eng. Sci., 115 (1927), 700–721. https://doi.org/10.1098/rspa.1927.0118 doi: 10.1098/rspa.1927.0118
[24]	R. M. Anderson, R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, UK, 1992. https://doi.org/10.1093/oso/9780198545996.001.0001
[25]	H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000), 599–653. https://doi.org/10.1137/S0036144500371907 doi: 10.1137/S0036144500371907
[26]	M. J. Keeling, P. Rohani, Modeling Infectious Diseases in Humans and Animals, Princeton University Press, UK, 2011. https://doi.org/10.2307/j.ctvcm4gk0
[27]	D. H. Anderson, Compartmental modeling and tracer kinetics, in Lecture Notes in Biomathematics, Springer-Verlag Berlin, Heidelberg, 1983. https://doi.org/10.1007/978-3-642-51861-4
[28]	R. Anguelov, J. Lubuma, Y. Dumont, Mathematical analysis of vector-borne diseases on plants, in IEEE, 4th International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications, Shanghai, China, (2012), 22–29. https://doi.org/10.1109/PMA.2012.6524808
[29]	I. M. Bulai, A. C. Esteves, F. Lima, E. Venturino, A mathematical modeling approach to assess biological control of an orange tree disease, Appl. Math. Lett. 118 (2021), 107–140. https://doi.org/10.1016/j.aml.2021.107140 doi: 10.1016/j.aml.2021.107140
[30]	J. Chuche, D. Thiéry, Biology and ecology of the flavescence dorée vector Scaphoideus titanus: a review, Agron. Sustainable Dev., 34 (2014), 381–403. https://doi.org/10.1007/s13593-014-0208-7 doi: 10.1007/s13593-014-0208-7
[31]	I. M. Lee, R. Gundersen, E. Dawn, R. Davis, I. Bartoszyk, Revised classification scheme of phytoplasmas based on RFLP analyses of 16S rRNA and ribosomal protein gene sequences, Int. J. Syst. Evol. Microbiol., 48 (1998), 1153–1169. https://doi.org/10.1099/00207713-48-4-1153 doi: 10.1099/00207713-48-4-1153
[32]	A. B. Santander, E. M. Rodríguez, C. D. Toapanta, R. A. Suárez, Vitis vinifera, a case of study at Chaupi Estancia, Pichincha province, Siembra, 9 (2022), e3731. https://doi.org/10.29166/siembra.v9i2.3731 doi: 10.29166/siembra.v9i2.3731
[33]	W. Sinclair, H. Griffiths, I. M. Lee, Mycoplasmalike organisms as causes of slow growth and decline of trees and shrubs, J. Arboric., 20 (1994), 176–189. https://doi.org/10.48044/jauf.1994.033 doi: 10.48044/jauf.1994.033
[34]	M. Maixner, R. C. Pearson, E. Boudon-Padieu, A. Caudwelland, Scaphoideus titanus, a possible vector of grapevine yellows in New York, Plant Dis., 77 (1993), 408–413. https://doi.org/10.1094/PD-77-0408 doi: 10.1094/PD-77-0408
[35]	M. Ripamonti, M. Pegoraro, M. Rossi, N. Bodino, D. Beal, L. Panero, et al., Prevalence of flavescence dorée phytoplasma-infected scaphoideus titanus in different vineyard agroecosystems of Northwestern Italy, Insects, 11 (2020), 301. https://doi.org/10.3390/insects11050301 doi: 10.3390/insects11050301
[36]	I. E. Rigamonti, M. Salvetti, P. Girgenti, P. A. Bianco, F. Quaglino, Investigation on flavescence dorée in north-western Italy identifies Map-M54 (16SrV-D/Map-FD2) as the only phytoplasma genotype in Vitis vinifera L. and reveals the presence of new putative reservoir plants, Biology, 12 (2023), 1216. https://doi.org/10.3390/biology12091216 doi: 10.3390/biology12091216
[37]	S. Tramontini, A. Delbianco, S. Vos, Pest survey card on flavescence dorée phytoplasma and its vector scaphoideus titanus, EFSA Supporting Publ., 17 (2020), 1909E. https://doi.org/10.2903/sp.efsa.2020.EN-1909 doi: 10.2903/sp.efsa.2020.EN-1909
[38]	M. Ripamonti, M. Pegoraro, C. Morabito, I. Gribaudo, A. Schubert, D. Bosco, et al., Susceptibility to flavescence dorée of different Vitis vinifera genotypes from north-western Italy, Plant Pathol., 77 (2021), 511–520. https://doi.org/10.1111/ppa.13301 doi: 10.1111/ppa.13301
[39]	R. Gaines, J. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Springer–Verlag, Berlin, Germany, 1977. https://doi.org/10.1007/BFb0089537
[40]	P. Benevieri, M. Furi, A simple notion of orientability for Fredholm maps of index zero between Banach manifolds and degree theory, Ann. Sci. Math. Québec, 22 (1998), 131–148.
[41]	G. Dinca, J. Mawhin, Brouwer degree: The core of nonlinear analysis, in Progress in Nonlinear Differential Equations and Their Applications, Birkhäuser Cham, Switzerland, 95 (2021). https://doi.org/10.1007/978-3-030-63230-4
[42]	A. Coronel, F. Huancas, M. Pinto, Sufficient conditions for the existence of positive periodic solutions of a generalized nonresident computer virus model, Quaestiones Math., 44 (2019), 259–279. https://doi.org/10.2989/16073606.2019.1686438 doi: 10.2989/16073606.2019.1686438
[43]	A. Coronel, F. Huancas, I. Hess, E. Lozada, F. Novoa-Muñoz, Analysis of a SEIR-KS mathematical model for computer virus propagation in a periodic environment, Mathematics, 8 (2020), 761. https://doi.org/10.3390/math8050761 doi: 10.3390/math8050761
[44]	A. Coronel, F. Huancas, S. Berres, Study of an epidemiological model for plant virus diseases with periodic coefficients, Appl. Sci., 14 (2024), 399. https://doi.org/10.3390/app14010399 doi: 10.3390/app14010399
[45]	J. Chuche, D. Thiery, Biology and ecology of the Flavescence dorée vector Scaphoideus titanus: A review, Agron. Sustainable Dev., 34 (2014), 355–377. https://doi.org/10.1007/s13593-014-0208-7 doi: 10.1007/s13593-014-0208-7
[46]	S. Tramontini, A. Delbianco, S. Vos, Pest survey card on flavescence dorée phytoplasma and its vector Scaphoideus titanus, EFSA Supporting Publ., 17 (2020), 36. https://doi.org/10.2903/sp.efsa.2020.EN-1909 doi: 10.2903/sp.efsa.2020.EN-1909
[47]	E. Boudon-Padieu, Cicadelle vectrice de la flavescence dorée, Scaphoideus Titanus, Ball, 1932, in Ravageurs de la vigne, Féret, Bordeaux, (2000), 110–120.
[48]	S. Malembic-Maher, P. Salar, L. Filippin, P. Carle, E. Angelini, X. Foissac, Genetic diversity of European phytoplasmas of the 16SrV taxonomic group and proposal of 'Candidatus Phytoplasma rubi', Int. J. Syst. Evol. Microbiol., 61 (2011), 2129–2134. https://doi.org/10.1099/ijs.0.025411-0 doi: 10.1099/ijs.0.025411-0

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