Plants possess innate resistance mechanisms, originating from their immune systems, to defend against pathogenic or viral invasions. This study presents a mathematical model, using nonlinear infection terms, designed to investigate plant resistance to mosaic virus, which is transmitted via whitefly vectors. The proposed model incorporates microbial biostimulants aimed at enhancing plant growth and stimulating immune responses to enhance disease resistance. Additionally, the model accounts for a time delay associated with the plant’s incubation period. The basic reproduction number, denoted as \( \boldsymbol{R_0} \) , is derived to characterize the system’s dynamics. Equilibrium points are identified, and their stability properties are rigorously analyzed. The influence of various parameters related to disease resistance is examined through both analytical and numerical approaches. The analysis reveals that the disease-free equilibrium remains stable when \( \boldsymbol{R_0 < 1} \) . In contrast, an endemic equilibrium emerges when \( \boldsymbol{R_0 > 1} \) , and the system exhibits Hopf bifurcation as a key parameter exceeds its critical threshold. Bubbling phenomena are observed when variations occur in the resistance rate and incubation period. The findings demonstrate that both the resistance rate and the application of microbial biostimulants play a stabilizing role in disease dynamics and enhance plant growth, whereas an increased infection rate tends to destabilize the system. Therefore, the results can help farmers with a strategic advantage in managing plant disease, crop health, and increasing crop productivity.
