Adaptive parameter-space refinement and Markov state models for eco-epidemiological dynamics.

We propose a computational framework that combines Adaptive Mesh Refinement in Parameter Space (AMR-PS), ensemble stochastic simulation, and Markov state model (MSM) coarse-graining to characterize metastable dynamics in an infection-predator-prey eco-epidemiological system. By adaptively refining regions near bifurcations, the strategy dramatically reduces the cost of exploring high-dimensional parameter spaces while preserving fidelity. Ensemble simulations capture the stochastic pathways connecting metastable states, highlighting regimes in which noise qualitatively reshapes basins of attraction. MSM coarse-graining supplies interpretable macrostates and transition matrices that permit efficient computation of quantities of interest, and that faithfully summarize long-time behavior. Applied to representative eco-epidemiological regimes, the workflow identifies parameter regions where stochasticity most realistically reflects the deterministic bifurcation structure, quantifies escape times between endemic and disease-extinction basins, and could provide practical diagnostics for ecological management. The method is scalable, modular, and applicable to multiscale problems where rare events and parametric sensitivity influence complex system dynamics.