Abstract: The identifiability of model parameters plays a crucial role in determining the precision of model predictions. Additionally, predictions based on identifiable outcomes exhibit a higher degree of scientific rigor and accuracy. Unlike ordinary differential systems, achieving parameter identifiability in age-structured models with initial-boundary conditions poses considerable challenges. This paper aims to investigate the structural and practical identifiability of an age-structured tuberculosis model with relapse. First, we employ the eigenvalue method to ascertain the order of unidentifiable parameters. In conjunction with data provided by the Public Health Science Data Center, we employ Monte Carlo simulation to explore the practical identifiability of the proposed model. By calculating the Average Relative Error (ARE) for each parameter and utilizing the Fisher information matrix, we determine that all parameters are identifiable. Furthermore, we assess how uncertainty in these parameters affects tuberculosis transmission by analyzing the Fisher information matrix and partial rank correlation coefficient.

Key words: tuberculosis, identifiable analysis, sensitivity analysis