This study investigates the transmission dynamics of a plant virus, which poses a significant threat to agricultural productivity and food security. The mathematical model is structured into subpopulations of plants—susceptible, exposed, infectious, and recovered—and incorporates both curative and preventive treatments through delay differential equations (DDEs). The dynamical analysis rigorously examines the key properties of the delayed model, including positivity, boundedness, existence, and uniqueness of solutions. The basic reproduction number is derived, and a sensitivity analysis of key parameters is conducted. Both local and global stabilities of the model are established around its two equilibria: the virus-free and virus-endemic states. Numerical simulations illustrate the behavior of the delayed model and demonstrate the effectiveness of incorporating delay-based strategies in controlling the virus within the plant population.

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Investigation of Virus Transmission in Plants by Using Time Delay Tool, Curative and Preventive Treatments

  • Ali Raza,
  • Nuno M. Brites,
  • Eugénio M. Rocha,
  • Muhammad Mohsin,
  • Zeeshan Haider

摘要

This study investigates the transmission dynamics of a plant virus, which poses a significant threat to agricultural productivity and food security. The mathematical model is structured into subpopulations of plants—susceptible, exposed, infectious, and recovered—and incorporates both curative and preventive treatments through delay differential equations (DDEs). The dynamical analysis rigorously examines the key properties of the delayed model, including positivity, boundedness, existence, and uniqueness of solutions. The basic reproduction number is derived, and a sensitivity analysis of key parameters is conducted. Both local and global stabilities of the model are established around its two equilibria: the virus-free and virus-endemic states. Numerical simulations illustrate the behavior of the delayed model and demonstrate the effectiveness of incorporating delay-based strategies in controlling the virus within the plant population.