WSEAS Transactions on Computers

Print ISSN: 1109-2750
E-ISSN: 2224-2872

Volume 18, 2019

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

A Multigrid Approximation to the Expansion of Xylella Fastidiosa in Almond Trees

AUTHORS: Maria Teresa Signes-Pont, Deivis Eduard Ramirez-Martinez, Juan Manuel García-Chamizo, Higinio Mora-Mora

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ABSTRACT: Xylella fastidiosa (X.F.) is a plant pathogen that is transmitted exclusively by sap insects that feed on xylem fluid. This paper presents a theoretical grid-model to approach the expansion of this bacterium in almond trees orchards. The model is based on a multigrid approximation defined by both the environmental characteristics that have an impact on the status of the trees and the time which depicts their evolution. The trees can be healthy (S), exposed (E), infected (I) or dead (D). The dynamics of each grid is defined by a set of update rules which determine the value of the cells in a particular neighbourhood. The preliminary results of this work allow us to provide a relationship between the environmental characteristics and the status of the trees as time passes. This is useful to guide the decision making on the eradication policies.

KEYWORDS: Xylella Fastidiosa, disease expansion, mathematical modelling, grid-model, neighbourhood, update rules


[ 1] Redak, R. A. et al. The biology of xylem fluid– feeding insect vectors of xylella fastidiosa and their relation to disease epidemiology. Annual Review of Entomology. 49 (1): 243–270. 2004.

[2] A. H. Purcell. 1980. Almond leaf scorch: Leafhopper and spittlebug vectors. J. Econ. Entomol. 73:834-838

[3] R. Krugner et al. Phenology of Xylella fastidiosa and Its Vector Around California Almond Nurseries: An Assessment of Plant Vulnerability to Almond Leaf Scorch Disease Plant Disease / Vol. 96 No. 10

[4] R. P. P. Almeida, Vector Transmission of Xylella fastidiosa: Applying Fundamental Knowledge to Generate Disease Management Strategies Xylella fastidiosa Vector Transmission Biology. Annals of the Entomological Society of America. Published by: Entomological Society of America

[5] EPPO (2016) Diagnostic PM 7/24 (2) Xylella fastidiosa. Bulletin OEPP/EPPO Bulletin (2016) 46 (3), 463–500

[6] EPPO (2016) PM 3/82 (1) Inspection of places of production for Xylella fastidiosa. Bulletin OEPP/EPPO Bulletin (2016) 46 (3), 407–418

[7] W.O. Kermack, A. G. McKendrick. Contributions to the mathematical theory of epidemics, part I. Proc Roy Soc Edin A 1927; 115: 700-21.

[8] Isea, R & Lonngren, K.E. On the Mathematical Interpretation of Epidemics by Kermack and McKendrick. Gen. Math. Notes, Vol. 19, No. 2, December 2013, pp. 83-87.

[9] Miller, Joel.C. Mathematical models of SIR disease spread with combined non-sexual and sexual transmission routes, Infectious Disease Modelling 2 (2017) 35-55.

[10] Decreusefond, L et al. Large graph limit for an SIR process in random network with heterogeneous connectivity. The Annals of Applied Probability, 22 (2) (2012), pp. 541- 575.

[11] Jianquan, L. and Zhien, M. Global Analysis of SIS Epidemic Models with Variable Total Population Size Mathematical and Computer Modelling 39 (2004) 1231-1242

[12] Shah, N.H. and Jyoti Gupta, J. SEIR Model and Simulation for Vector Borne Diseases. Applied Mathematics, 2013, 4, 13-17

[13] M.T. Signes-Pont et al. A discrete approach of the Susceptible-Infectious-Susceptible (SIS) Model of Disease Expansion. International Journal of Computers (2017) available at

[14] M.T. Signes Pont et al., The SusceptibleInfectious-Recovered (SIR) model of disease expansion: a new approach. Proc. of the 17th Mathematical Modelling Conference, 2017.

[15] M.T. Signes Pont, M.T. at al., The SusceptibleInfectious Model of Disease Expansion analysed under the scope of connectivity and neighbor rules. Computer Science & Information Technology (CS & IT) 7 (1): 1-10, 2017.

[16] M.T. Signes Pont, M.T. at al. Modelling the malware propagation in mobile computer devices. Computers & Security, Volume 79, November 2018, Pages 80-93

WSEAS Transactions on Computers, ISSN / E-ISSN: 1109-2750 / 2224-2872, Volume 18, 2019, Art. #3, pp. 19-30

Copyright © 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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