Tutorial Article
Structural identifiability and observability of compartmental models of the COVID-19 pandemic

https://doi.org/10.1016/j.arcontrol.2020.12.001Get rights and content

Highlights

  • Structural identifiability and observability are desirable model properties.

  • They describe a model’s ability to inform about unmeasured parameters and states.

  • We collect and analyse hundreds of compartmental models of the COVID-19 pandemics.

  • We show which parameters and states can be determined from output measurements.

  • We discuss how to choose the most informative model for the available knowledge.

Abstract

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.

Keywords

Identifiability
Observability
Dynamic modelling
Epidemiology
COVID-19

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This research has received funding from the Spanish Ministry of Science, Innovation and Universities and the European Union FEDER under project grant SYNBIOCONTROL (DPI2017-82896-C2-2-R) and the CSIC, Spain intramural project grant MOEBIUS (PIE 202070E062). The funding bodies played no role in the design of the study, the collection and analysis of the data or in the writing of the manuscript.

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