Detection of a very serious error in the paper: "On identifiability of nonlinear ODE models and applications in viral dynamics"

TL;DR

The paper addresses the identifiability of a widely used nonlinear ODE HIV model with a time-varying parameter $\eta$ and challenges the prior claim that all parameters are locally identifiable. It uses a $\tau$-parameterized transformation to demonstrate non-uniqueness of $\delta$, $N$, and $\eta$, and analyzes a foundational error in the previous identifiability proof by exposing a misapplied Jacobian argument. The erratum identifies two typos in Eq. (6.23) and shows that treating outputs and their derivatives as independent inflates the apparent rank, thereby invalidating the claimed identifiability of all parameters. This work clarifies the true identifiability status of the HIV model and underscores the need for correct application of identifiability methods, connecting to broader frameworks like unknown-input observability in later literature.

Abstract

This erratum highlights a very serious error in a paper published by SIAM Review in 2011. The error is in Section 6.2 of [1]. It is very important to notify this error because of the following two reasons: (i) [1] is one of the most cited contributions in the field of identifiability of viral dynamics models, and (ii)the error is relevant because, as a result of it, a very popular viral model (perhaps the most popular in the field of HIV dynamics) has been classified as identifiable. In contrast, three of its parameters are not identifiable, even locally. This erratum first proves the non uniqueness of the three unidentifiable parameters by exhibiting infinitely many distinct but indistinguishable values of them. The non uniqueness is even local. Then, this erratum details the error made by the authors of [1] which produced the claimed (but false) local identifiability of all the model parameters.