Structural and practical identifiability of an immuno-hand foot and mouth disease model integrating immune response within a host.

In this work, we extend the nested modeling framework to establish an immuno-epidemiological model for Hand Foot and Mouth Disease (HFMD). This model intricately links host-to-host transmission, virus release, and recovery rates to within-host immune system dynamics. We introduce an ordinary differential equation (ODE)-based within-host model and an partial differential equation (PDE)-based between-host model. Utilizing sensitivity-based locally structural identifiability methods, including principal component analysis (PCA) and eigenvalue analysis, we systematically prioritize parameters from least to most identifiable. Furthermore, we perform globally structural identifiability analysis using differential algebra methods, demonstrating global identifiability of within-host parameters under specific conditions. Leveraging these results, we accurately estimate model parameters using experimental data. Monte Carlo simulations (MCS) reveal practical unidentifiable parameters, indicating that the multi-scale immuno-epidemiological HFMD model is both locally and practically unidentifiable. Finally, sensitivity analysis reveals that within host kinetics considerably influences the temporal dynamics of the HFMD model at the population level.