Ordinary differential equation models are widely used to understand and forecast complex dynamical systems, but their predictive value depends on reliable parameter estimation. Structural identifiability assesses whether parameters can be uniquely recovered from ideal observations, whereas practical identifiability depends on finite, noisy and partially observed data. We introduce the Practical Identifiability Index (PII), a marginal uncertainty-width metric based on the logarithmic span of confidence intervals. Expressed on an order-of-magnitude scale, the PII summarises how tightly individual positive-valued parameters are constrained by available observations, enabling comparison across parameters, models, error structures and observation designs. The PII is intended as a complementary diagnostic, not a standalone identifiability test, and should be interpreted alongside coverage, profile likelihoods, posterior summaries, sensitivity analysis or structural identifiability results. Using parametric bootstrap experiments across growth and compartmental epidemic models, we identify consistent principles: uncertainty decreases as calibration windows become more informative, increases with observation noise and parameter coupling, and remains high for latent or indirectly observed processes. Parameters governing early observable dynamics become constrained sooner, while additional observables can improve constraint for latent progression and recovery parameters. The PII provides a simple, reportable summary of marginal parameter uncertainty for dynamical modelling.

翻译：常微分方程模型广泛应用于理解和预测复杂动态系统，但其预测价值依赖于可靠的参数估计。结构可辨识性评估参数能否从理想观测中唯一恢复，而实用可辨识性则取决于有限、含噪声且部分观测的数据。我们提出了实用可辨识性指数（PII），一种基于置信区间对数跨度的边际不确定性宽度度量。以数量级尺度表达时，PII总结了单个正值参数受可用观测约束的紧密程度，从而能够跨参数、跨模型、跨误差结构和跨观测设计进行比较。PII旨在作为补充诊断工具，而非独立可辨识性检验，需与覆盖率、剖面似然、后验摘要、敏感性分析或结构可辨识性结果结合解读。通过生长模型和房室流行病模型的参数自助法实验，我们识别出一致性原则：当校准窗口信息量更大时，不确定性降低；随观测噪声和参数耦合增加而升高；对潜在或间接观测过程则持续较高。支配早期可观测动态的参数约束更快形成，而额外观测变量可改善潜在进程和恢复参数的约束。PII为动态建模提供了简单、可报告的边际参数不确定性总结。