Page 7 - IJOCTA-15-1

An International Journal of Optimization and Control: Theories & Applications
ISSN: 2146-0957 eISSN: 2146-5703
Vol.15, No.1, pp.1-13 (2025)
https://doi.org/10.36922/ijocta.1507

RESEARCH ARTICLE

A nonlinear mathematical model to describe the transmission
dynamics of the citrus canker epidemic

Pushpendra Kumar 1,2*

1 Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, T¨urkiye
2 Department of Mathematics, Mathematics Research Center, Near East University TRNC, Mersin 10, T¨urkiye
kumarsaraswatpk@gmail.com

ARTICLE INFO ABSTRACT

Article History: In this article, a mathematical model is proposed to define the transmission
Received 24 December 2023 dynamics of one of the most dangerous plant diseases, citrus canker, by using
Accepted 5 July 2024 integer and fractional derivatives. For the fractional-order generalisation, the
Available Online 17 January 2025 well-known Caputo fractional derivative is used with the singular-type kernel.
The basic features of the proposed integer- and fractional-order models are
Keywords:
defined by using well-known mathematical concepts. The proposed model is
Citrus canker
numerically solved by using the Chebyshev spectral collocation scheme. Some
Bacterial epidemics
graphical justifications are also given to visualise the disease transmission in
Mathematical model
the population of citrus plants over time. This research study contains the
Caputo fractional derivative
first non-linear mathematical model of citrus canker transmission, which is the
Chebyshev spectral collocation
main novelty of this article.
scheme
AMS Classification 2010:
26A33; 65D30; 92D25; 93A30

1. Introduction are the factors that disseminate the citrus canker
diseases. 2–4

Citrus canker is a disease that affects citrus trees
such as lemon, orange, key lime, pomelo, grape- A number of research articles have been written
fruit, and other citrus fruits. Xanthomonas ax- to analyse the outbreaks of citrus canker. A study
onopodis is the causal agent. Citrus canker is on the cases of citrus canker in Florida was given
5
favoured by mild temperatures in between 20 and in ref. The outbreaks of citrus canker in nurs-
7
6
30 degrees Celsius, rainy weather or humidity, eries in Argentina were given in. In, the au-
high winds, heavy rain, and citrus leafminer dam- thors gave brief information on citrus canker in
8
age. This disease was first recognised in South- Brazil. In, the incidence of canker diseases in
east Asia, specifically India. Because of its fast the United States was discussed. A study on the
spread, it is a bacterial epidemic that has created control of citrus canker and citrus bacterial spots
9
1
endemics in many regions (see fig. 1). It has the with bacteriophages was proposed in ref. In, 10
ability to harm or infect all of the citrus-growing the genome editing of the epidemic susceptibil-
fields in the area. As a result, it has the poten- ity gene Cs LOB 1 in citrus confers resistance
tial to inflict significant ecological harm on citrus to citrus canker has been discussed. Some novel
plant species. The most common symptoms of results to understand the management of Xan-
this disease are lesion formation on the leaves and thomonas citri ssp. citri pathogenesis and citrus
fruit-rind blemishing. Plant-to-plant dissemina- canker epidemic are justified in. 11 A UAV-based
tion, improper vegetation, environmental factors remote sensing method to capture citrus canker
like wind, rain, insect vectors, and water splashing disease using machine learning and hyperspectral
*Corresponding Author
1