A Nonlinear Mathematical Model to Describe the Transmission Dynamics of the Citrus Canker Epidemic

Abstract

In this article, a mathematical model is proposed to define the transmission dynamics of one of the most dangerous plant diseases, citrus canker, by using integer and fractional derivatives. For the fractional-order generalisation, the well-known Caputo fractional derivative is used with the singular-type kernel. The basic features of the proposed integer- and fractional-order models are defined by using well-known mathematical concepts. The proposed model is numerically solved by using the Chebyshev spectral collocation scheme. Some graphical justifications are also given to visualise the disease transmission in the population of citrus plants over time. This research study contains the first non-linear mathematical model of citrus canker transmission, which is the main novelty of this article. © 2025 Elsevier B.V., All rights reserved.