Identifiability of a mathematical model plays a crucial role in parameterization of the model. In this study, we establish the structural identifiability of a Susceptible-Exposed-Infected-Recovered (SEIR) model given different combinations of input data and investigate practical identifiability with respect to different observable data, data frequency, and noise distributions. The practical identifiability is explored by both Monte Carlo simulations and a Correlation Matrix approach. Our results show that practical identifiability benefits from higher data frequency and data from the peak of an outbreak. The incidence data gives the best practical identifiability results compared to prevalence and cumulative data. In addition, we compare and distinguish the practical identifiability by Monte Carlo simulations and a Correlation Matrix approach, providing insights for when to use which method for other applications.

翻译：数学模型的参数可辨识性在模型参数化中起着关键作用。本研究针对易感-暴露-感染-康复（SEIR）模型，建立了不同输入数据组合下的结构可辨识性，并探讨了模型在不同观测数据、数据频率及噪声分布条件下的实际可辨识性。我们通过蒙特卡洛模拟和相关矩阵方法对实际可辨识性进行了分析。结果表明，提高数据频率并采用疫情峰值阶段的数据有助于增强实际可辨识性。与患病率数据和累积数据相比，发病率数据能获得最佳的实际可辨识性结果。此外，我们比较并区分了蒙特卡洛模拟和相关矩阵方法所揭示的实际可辨识性，为在其他应用中如何选择合适方法提供了参考依据。