Effective application of mathematical models to interpret biological data and make accurate predictions often requires that model parameters are identifiable. Requisite to identifiability from a finite amount of noisy data is that model parameters are first structurally identifiable: a mathematical question that establishes whether multiple parameter values may give rise to indistinguishable model outputs. Approaches to assess structural identifiability of deterministic ordinary differential equation models are well-established, however tools for the assessment of the increasingly relevant stochastic and spatial models remain in their infancy.

I provide in this talk an introduction to structural identifiability, before presenting new frameworks for the assessment of stochastic and partial differential equations. Importantly, I discuss the relevance of our methodology to model selection, and more the practical and aptly named practical identifiability of parameters in the context of experimental data. Finally, I conclude with a brief discussion of future research directions and remaining open questions.