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：数学模型的辨识性在模型参数化中起着关键作用。本研究基于不同的输入数据组合，确立了易感-暴露-感染-康复（SEIR）模型的结构可辨识性，并针对不同的可观测数据、数据频率及噪声分布探究了实际可辨识性。通过蒙特卡罗模拟和相关矩阵方法共同探索了实际可辨识性。结果表明，较高的数据频率及来自疫情峰值的数据有助于提升实际可辨识性，其中发病率数据相比患病率和累积数据能够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罗模拟与相关矩阵方法在实际可辨识性方面的差异，为其他应用场景中方法的选择提供了参考依据。