Modeling and perturbation analysis of plant disease dynamics: a novel HLDCT framework for fire blight management

Plant diseases, such as fire blight, pose significant economic threats to the agricultural sector. While mathematical models are crucial for understanding their spread, they often simplify the complex management practices used in the field. This paper introduces a novel five-compartment differential equation model, termed the HLDCT model (Healthy, Latent, Diseased, Controlled, Terminated), to provide a more agriculturally relevant framework. The key innovation is the explicit separation of a ‘Controlled’ state, representing tissues under active management, from a ‘Terminated’ state, which represents tissues that have been fully removed or recovered. We analyze the model’s stability and basic reproduction number ($R_{0}$) and conduct a comprehensive suite of perturbation analyses, including sensitivity, structural, stochastic, and control-oriented approaches, to evaluate its robustness and derive management insights. Our analysis, applied to a fire blight case study, demonstrates that proactive management strategies significantly reduce disease burden. Sensitivity analysis identified the transmission rate (τ) and the influx of new susceptible tissue (Π) as the most influential parameters on the basic reproduction number ($R_{0}$). Structural perturbation analysis revealed that a direct infection pathway, bypassing the latent stage, poses the greatest epidemic risk, increasing $R_{0}$ by 160%. The HLDCT model and its thorough analysis provide a more nuanced platform for evaluating integrated pest management (IPM) strategies and translating theoretical findings into actionable agricultural guidance.