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The successful application of epidemic models hinges on our ability toestimate model parameters from limited observations reliably. Anoften-overlooked step before estimating model parameters consists of ensuringthat the model parameters are structurally identifiable from the observedstates of the system. In this tutorial-based primer, intended for a diverseaudience, including students training in dynamic systems, we review and providedetailed guidance for conducting structural identifiability analysis ofdifferential equation epidemic models based on a differential algebra approachusing DAISY (Differential Algebra for Identifiability of SYstems) and\textit{Mathematica} (Wolfram Research). This approach aims to uncover anyexisting parameter correlations that preclude their estimation from theobserved variables. We demonstrate this approach through examples, includingtutorial videos of compartmental epidemic models previously employed to studytransmission dynamics and control. We show that the lack of structuralidentifiability may be remedied by incorporating additional observations fromdifferent model states, assuming that the system's initial conditions areknown, using prior information to fix some parameters involved in parametercorrelations, or modifying the model based on existing parameter correlations.We also underscore how the results of structural identifiability analysis canhelp enrich compartmental diagrams of differential-equation models byindicating the observed state variables and the results of the structuralidentifiability analysis.

Structural identifiability analysis of epidemic models based on differential equations: A tutorial-based primer