<p>In this article, a mathematical model is derived to investigate the dynamics and control of whitefly-borne mosaic disease, incorporating plant resistance to the mosaic virus. The model incorporates both microbial biostimulants and roguing as disease control measures. The infection rate is assumed to be a decreasing function of both the application of biostimulants and the rate of plant resistance. Equilibrium points of the system are identified, and their stability properties are analyzed. Then the basic reproduction number is derived, which is a decreasing function of biostimulants and roguing. Stability analysis reveals that the disease-free equilibrium is locally asymptotically stable when the basic reproduction number is less than one. In contrast, the endemic equilibrium exists when the basic reproduction number is greater than unity. It exhibits Hopf bifurcation when the infection rate exceeds a critical value. Moreover, the bubbling phenomenon is observed in response to variations in the resistance rate. Finally, optimal control theory is employed to determine the most effective rates of biostimulants and roguing, aiming to minimize the disease in a cost-effective way. The results demonstrate that the application of biostimulants can stabilize the endemic equilibrium and facilitate the transition to a disease-free steady state. The optimal control approach determines the optimal use of biostimulants and roguing that minimizes the infection in an economically viable way.</p>

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Mosaic disease dynamics with microbial biostimulants and roguing: modelling disease resistance and optimal control

  • Tarak Nath Halder,
  • Fahad Al Basir,
  • Khalid Aldawsari,
  • Aeshah A. Raezah

摘要

In this article, a mathematical model is derived to investigate the dynamics and control of whitefly-borne mosaic disease, incorporating plant resistance to the mosaic virus. The model incorporates both microbial biostimulants and roguing as disease control measures. The infection rate is assumed to be a decreasing function of both the application of biostimulants and the rate of plant resistance. Equilibrium points of the system are identified, and their stability properties are analyzed. Then the basic reproduction number is derived, which is a decreasing function of biostimulants and roguing. Stability analysis reveals that the disease-free equilibrium is locally asymptotically stable when the basic reproduction number is less than one. In contrast, the endemic equilibrium exists when the basic reproduction number is greater than unity. It exhibits Hopf bifurcation when the infection rate exceeds a critical value. Moreover, the bubbling phenomenon is observed in response to variations in the resistance rate. Finally, optimal control theory is employed to determine the most effective rates of biostimulants and roguing, aiming to minimize the disease in a cost-effective way. The results demonstrate that the application of biostimulants can stabilize the endemic equilibrium and facilitate the transition to a disease-free steady state. The optimal control approach determines the optimal use of biostimulants and roguing that minimizes the infection in an economically viable way.