This study focuses on the transmission dynamics of anthracnose disease and the effectiveness of treatment strategies designed to limit its spread, particularly under splashing-rain conditions. A mathematical model is developed to investigate the progression of anthracnose in a healthy environment when incorporating control measures such as treatment interventions and systematic removal of infected plants. The model is extended to a fractional-order form using the fractal–fractional operator, allowing continuous monitoring and reliable numerical approximations. A detailed analysis is performed to examine stability, boundedness, and uniqueness, thereby ensuring the validity of the system dynamics. Transmission rates across sub-compartments are derived through global derivatives and verified using Lipschitz and linear growth conditions. Bifurcation analysis is conducted to assess the emergence and control of chaotic behavior within the system. The role of the fractional operator, including the Mittag–Leffler kernel in its generalized form, is studied via a two-step Lagrange polynomial approach. Numerical simulations illustrate the influence of various factors on disease spread and demonstrate the effectiveness of hypersensitive response strategies in controlling infections. The findings contribute to a deeper understanding of anthracnose transmission and support the development of mathematically verified management strategies for improved plant health.
Faiz et al. (Thu,) studied this question.