Bifurcation and control of xanthomonas infectious disease spread in banana plants under hypersensitive response

Examining the model of banana xanthomonas disease with treatment to stop the infections from spreading across the community due to pathogen attack is the main goal of this research. In order to examine the recovery rate of banana xanthomonas after taking control measures with treatment and continuous cutting of infected one, a mathematical model is established using the created hypothesis for healthy environment and the Fractal–Fractional operator is utilized to convert the model into a fractional-order model for continuous monitoring including reliable numerical solutions. In order to ascertain the stable status of the recently built fractional-order system, a qualitative and quantitative analysis is also conducted. Reliable results are ensured by examining the boundedness and uniqueness of the model, which are crucial attributes for comprehending the intricate dynamics. The global derivative is used to determine the rate of disease effects according to each sub-compartment and is validated for genuine positivity using linear growth and Lipschitz conditions. The global stability of the system is investigated using Lyapunov’s first derivative functions in order to evaluate the overall effect of the disease’s spread and control. The impacts of different parameters on the sickness are illustrated using numerical simulations, which are used to explore the effect of the fractional operator on the generalized form of the Mittag–Leffler kernel utilizing a two-step Lagrange polynomial approach for continuous monitoring. Simulations have been made to see the real behavior and control of xanthomonas disease caused by pathogen attack by taking control measures for healthy environment with hypersensitive response. Also, it can be observed the continuous monitoring with dimensional effects helps for identification of infected banana plants and can be removed by cutting process. This kind of research will be beneficial in determining how diseases spread and in creating control plans based on our validated findings for banana plants.