The recent coronavirus disease (COVID-19) outbreak has dramatically increased the public awareness and appreciation of the utility of dynamic models. At the same time, the dissemination of contradictory model predictions has highlighted their limitations. If some parameters and/or state variables of a model cannot be determined from output measurements, its ability to yield correct insights – as well as the possibility of controlling the system – may be compromised. Epidemic dynamics are commonly analysed using compartmental models, and many variations of such models have been used for analysing and predicting the evolution of the COVID-19 pandemic. In this paper we survey the different models proposed in the literature, assembling a list of 36 model structures and assessing their ability to provide reliable information. We address the problem using the control theoretic concepts of structural identifiability and observability. Since some parameters can vary during the course of an epidemic, we consider both the constant and time-varying parameter assumptions. We analyse the structural identifiability and observability of all of the models, considering all plausible choices of outputs and time-varying parameters, which leads us to analyse 255 different model versions. We classify the models according to their structural identifiability and observability under the different assumptions and discuss the implications of the results. We also illustrate with an example several alternative ways of remedying the lack of observability of a model. Our analyses provide guidelines for choosing the most informative model for each purpose, taking into account the available knowledge and measurements.

A dynamic model is structurally identifiable (respectively, observable) if it is theoretically possible to infer its unknown parameters (respectively, states) by observing its output over time. The two properties, structural identifiability and observability, are completely determined by the model equations. Their analysis is of interest for modellers because it informs about the possibility of gaining insight into a model’s unmeasured variables. Here we cast the problem of analysing structural identifiability and observability as that of finding Lie symmetries. We build on previous results that showed that structural unidentifiability amounts to the existence of Lie symmetries. We consider nonlinear models described by ordinary differential equations and restrict ourselves to rational functions. We revisit a method for finding symmetries by transforming rational expressions into linear systems. We extend the method by enabling it to provide symmetry-breaking transformations, which allows for a semi-automatic model reformulation that renders a non-observable model observable. We provide a MATLAB implementation of the methodology as part of the STRIKE-GOLDD toolbox for observability and identifiability analysis. We illustrate the use of the methodology in the context of biological modelling by applying it to a set of problems taken from the literature.

Mechanistic dynamic models of biological systems allow for a quantitative and systematic interpretation of data and the generation of testable hypotheses. However, these models are often over-parameterized, leading to nonidentifiability and nonobservability, that is, the impossibility of inferring their parameters and state variables. The lack of structural identifiability and observability (SIO) compromises a model's ability to make predictions and provide insight. Here we present a methodology, AutoRepar, that corrects SIO deficiencies of nonlinear ODE models automatically, yielding reparameterized models that are structurally identifiable and observable. The reparameterization preserves the mechanistic meaning of selected variables, and has the exact same dynamics and input-output mapping as the original model. We implement AutoRepar as an extension of the STRIKE-GOLDD software toolbox for SIO analysis, applying it to several models from the literature to demonstrate its ability to repair their structural deficiencies. AutoRepar increases the applicability of mechanistic models, enabling them to provide reliable information about their parameters and dynamics.

The recent coronavirus disease (COVID-19) outbreak has dramatically increased the public awareness and appreciation of the utility of dynamic models. At the same time, the dissemination of contradictory model predictions has highlighted their limitations. If some parameters and/or state variables of a model cannot be determined from output measurements, its ability to yield correct insights -as well as the possibility of controlling the system -may be compromised. Epidemic dynamics are commonly analysed using compartmental models, and many variations of such models have been used for analysing and predicting the evolution of the COVID-19 pandemic. In this paper we survey the different models proposed in the literature, assembling a list of 36 model structures and assessing their ability to provide reliable information. We address the problem using the control theoretic concepts of structural identifiability and observability. Since some parameters can vary during the course of an epidemic, we consider both the constant and time-varying parameter assumptions. We analyse the structural identifiability and observability of all of the models, considering all plausible choices of outputs and time-varying parameters, which leads us to analyse 255 different model versions. We classify the models according to their structural identifiability and observability under the different assumptions and discuss the implications of the results. We also illustrate with an example several alternative ways of remedying the lack of observability of a model. Our analyses provide guidelines for choosing the most informative model for each purpose, taking into account the available knowledge and measurements.

A recent paper published in PLOS Computational Biology [1] introduces the Scaling Invariance Method (SIM) for analysing structural local identifiability and observability. These two properties define mathematically the possibility of determining the values of the parameters (identifiability) and states (observability) of a dynamic model by observing its output. In this note we warn that SIM considers scaling symmetries as the only possible cause of non-identifiability and non-observability. We show that other types of symmetries can cause the same problems without being detected by SIM, and that in those cases the method may lead one to conclude that the model is identifiable and observable when it is actually not.