A New Insight into the Threshold and Oscillatory Regimes in Plant-Pathogen Models: A Nutrient-Driven Approach.

Abstract

Across ecosystems, autotroph growth and susceptibility to disease are strongly constrained by the availability of essential nutrients such as nitrogen and phosphorus. Understanding how nutrient availability influences disease transmission is important for predicting disease persistence, outbreak risk, and long-term ecosystem dynamics under changing environmental conditions. At the same time, infectious diseases in autotrophs can reshape ecosystem processes by altering elemental recycling and the nutrient supply available to hosts. Here, we formulate a five-dimensional deterministic system of nonlinear ordinary differential equations within a disease-mediated nutrient dynamic framework. We incorporate novel nutrient-driven transmission and nonlinear resource uptake kinetics to capture the bidirectional relationships linking elemental cycles with infectious disease in a natural forest ecosystem. Using a combination of qualitative mathematical analysis, including proofs of solutions boundedness and derivations of basic reproductive number, and numerical bifurcation analyses, we evaluate the system's long-term behavior. Our results show that nutrient-disease feedbacks strongly regulate the distribution of host densities and nutrients between autotrophs and the abiotic environment. Incorporating nutrient-driven transmission reveals bifurcation structures distinct from frameworks with constant transmission, highlighting high sensitivity to nutrient availability and stronger nonlinear feedbacks. Bifurcation analyses indicate that nutrient enrichment lowers the transmission threshold for disease persistence and accelerates the onset of oscillatory dynamics with greater amplitude under high nutrient levels. Similarly, higher transmission rates reduce the nutrient threshold for disease persistence and shift oscillatory dynamics to emerge at lower nutrient levels. We further show that even small differences in infected host uptake rates strongly influence dynamics: lower uptake dampens oscillations and weakens feedbacks, whereas higher uptake amplifies bottom-up nutrient effects on disease and reinforces top-down effects on nutrient cycling, producing pronounced limit cycles in hosts, nutrients, and prevalence. Overall, nutrient-driven transmission alters thresholds and oscillatory regimes in ecosystem disease models, leading to dynamics that are not captured under constant transmission assumptions. This work advances applied ecosystem and ecological disease sciences by improving our understanding of disease transmission processes in plant communities.