<p>The immuno-epidemiological model bridges immunology and epidemiology, offering a detailed framework for studying infectious disease dynamics. However, its high complexity, particularly in constructing Lyapunov functions for partial differential equation (PDE) systems, poses significant challenges in analyzing global stability. In this study, we propose a novel method to infer the Lyapunov function of the PDE system from its degenerate ordinary differential equation (ODE) counterpart, enabling rigorous analysis of the global stability of the between-host (epidemiological) model. Moreover, in the study of inverse problems, the given observational data may have multiple possible solutions. For differential equation models, the model’s identifiability is a prerequisite to ensuring the reliability of parameter estimation. To address identifiability issues in inverse problems, we introduce a method to transform the PDE system with integral terms into an ODE system, facilitating the application of structural identifiability techniques. Our work provides a powerful theoretical and practical framework for advancing the analysis and reliability of immuno-epidemiological models.</p>