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Dynamical analysis, infections in plants, and preventive policies utilizing the theory of fractional calculus

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Abstract

Farmers are trying to adopt new cultivation methods and technologies to produce more and good yield. Low productivity is due to a variety of factors; one of the main reasons is the existence of plant diseases spread by insects and pathogens. Infection in the plants of red chilli via the yellow virus is a current issue for the farmers. Here, we construct a model for the propagation of the yellow virus in the plants of red chilli to investigate the key factors. The proposed model is then presented in the framework of fractional derivative for more accurate findings. By applying the method of next-generation matrix, we determine the basic reproduction number \({\mathcal {R}}_0\). The recommended model is investigated for biological meaningful results. Moreover, we focus on the dynamical behavior and qualitative analysis of the yellow virus infection in the plants of red chili. Schaefer and Banach fixed-point theorems are utilized to demonstrate the uniqueness and existence of the solution of the recommended system. We find suitable circumstances for the Ulam–Hyers stability of the recommended system of plants infection. The solution routes are examined using a unique numerical method to highlight the contribution of the input factors on yellow virus dynamics. Key factors of the system are investigated numerically through different simulations. The most critical factors of the infection are highlighted to the policymakers for the prevention of the losses.

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Authors and Affiliations

  1. Department of Pathogenic Microbiology and Immunology, School of Basic Medical Sciences, Xian Jiaotong University Health Science Center, 76 West Yanta Road, Xian, 710061, China

    Asif Jan

  2. Department of Mathematics, College of Sciences and Arts, Qassim University, ArRass, Saudi Arabia

    Salah Boulaaras

  3. School of Mathematical Sciences, Universiti Sains Malaysia (USM), 11800, Penang, Malaysia

    Farah Aini Abdullah

  4. Department of Mathematics, University of Swabi, Swabi, KPK, 23561, Pakistan

    Rashid Jan

Authors
  1. Asif Jan
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  2. Salah Boulaaras
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  4. Rashid Jan
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Contributions

AJ and FAA conceptualized, investigated, analyzed, and validated the research; while, SB and RJ formulated, investigated, numerically examined, reviewed, and supervised this research work.

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Correspondence to Salah Boulaaras.

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Jan, A., Boulaaras, S., Abdullah, F.A. et al. Dynamical analysis, infections in plants, and preventive policies utilizing the theory of fractional calculus. Eur. Phys. J. Spec. Top. 232, 2497–2512 (2023). https://doi.org/10.1140/epjs/s11734-023-00926-1

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