Structural and practical identifiability of within-host models of virus dynamics - a review

Within-host mechanistic mathematical models of virus dynamics described by ordinary differential equations are most useful when linked to empirical data. The main challenge in estimating parameters from typically available, noisy data arises from the intrinsic parameter correlations induced by model structure. As a result, the optimization problem, which fits parameters by minimizing the distance between the model and the data, may admit infinitely many solutions. These challenges can be elucidated through the study of structural and practical identifiability of the proposed model. In this article, we review existing methods for the structural and practical identifiability of the basic within-host model of viral dynamics and provide guidelines for improving unidentifiability. We discuss the challenges and new developments in extending these techniques to non-ordinary within-host differential equation models (delay, partial, and stochastic) and stress the importance of using practical identifiability results to guide optimal experimental design.