Modeling, Analysis, and Transmission Dynamics of Cassava Mosaic Disease Through Stochastic Fractional Delay Differential Equations

Feliz Minhós (), Ali Raza (), Umar Shafique and Muhammad Mohsin
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Feliz Minhós: Department of Mathematics, School of Science and Technology, University of Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal
Ali Raza: Center for Research in Mathematics and Applications (CIMA), Institute for Advanced Studies and Research (IIFA), University of Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal
Umar Shafique: Department of Mathematics, National College of Business Administration and Economics, Lahore 54600, Pakistan
Muhammad Mohsin: Department of Mathematics, Technische Universitat Chemnitz, 62, 09111 Chemnitz, Germany

Mathematics, 2025, vol. 13, issue 3, 1-19

Abstract: Cassava is the sixth most important food crop worldwide and the third most important source of calories in the tropics. More than 800 million people depend on this plant’s tubers and sometimes leaves. To protect cassava crops and the livelihoods depending on them, we developed a stochastic fractional delayed model based on stochastic fractional delay differential equations (SFDDEs) to analyze the dynamics of cassava mosaic disease, focusing on two equilibrium states, the state of being absent from cassava mosaic disease and the state of being present with cassava mosaic disease. The basic reproduction number and sensitivity of parameters were estimated to characterize the level beyond which cassava mosaic disease prevails or declines in the plants. We analyzed the stability locally and globally to determine the environment that would ensure extinction and its persistence. To support the theoretical analysis, as well as the reliable results of the model, the present study used a nonstandard finite difference (NSFD) method. This numerical method not only improves the model’s accuracy but also guarantees that cassava mosaic probabilities are positive and bounded, which is essential for the accurate modeling of the cassava mosaic processes. The NSFD method was applied in all the scenarios, and it was determined that it yields adequate performance in modeling cassava mosaic disease. The ideas of the model are crucial for exploring key variables, which affect the scale of cassava mosaic and the moments of intervention. The present work is useful for discerning the mechanism of cassava mosaic disease as it presents a solid mathematical model capable of determining the stage of cassava mosaic disease.

Keywords: cassava mosaic disease; stochastic fractional delay differential equations; existence and uniqueness; stability results; extinction and persistence; NSFD; results (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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