Stability and control of a plant epidemic model with pesticide intervention

Abstract

This paper introduces a model for studying plant epidemics that applies pesticides to control disease spread among two types of plant populations: those that are susceptible and those that are already infected. The model uses non-linear ordinary differential equations and the Holling type II response function to depict how disease spreads based on the number of susceptible plants available. The model is carefully checked for biological accuracy, ensuring characteristics such as positivity and boundedness. It defines points of equilibrium where the numbers of susceptible and infected plants stabilize. The study looks at scenarios with no infected plants (disease-free equilibrium) and scenarios where the disease continues to exist within the plant population (endemic equilibrium). The basic reproduction number, R0, is calculated to assess the system's stability. If R0 is less than 1, the disease is unlikely to spread widely, and the system is likely to return to being disease-free, both locally and globally, over time. However, if R0 is greater than 1, it indicates that the disease will persist in the population. This endemic state has also been shown to be stable both locally and globally. A sensitivity analysis helps identify key factors that affect disease spread and assists in forming strategies to manage the disease. Finally, numerical simulations are used to support the findings of the analysis.