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

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.

An integrated framework for building trustworthy data-driven epidemiological models: Application to the COVID-19 outbreak in New York City

“…sufficient for our approach of minimizing the loss function (14), and the parameters are indeed close to constant in every stage. As a result, the parameter estimation is reliable.…”

“…Non-identifiability is a problem frequently encountered in pandemics modeling since, typically, not every state variable is available. In recent literature, model identifiability issues have been studied due to the wide variation in model projections in the context of the COVID-19 pandemic [ 2 , 14 – 16 ]. Tuncer et al analyzed the structural and practical identifiability of some of the most widely-used pandemic models, including SIR, SIR with treatment, and SEIR, assuming only one observed data type is available using simulated data [ 17 ].…”

“…They found that complex mechanistic models are more likely to have identifiability issues compared to simpler models. Massoni et al provided a systematical structural identifiability and observability analysis of 255 available compartmental models for COVID-19 and found that approximately one-third of them have structurally non-identifiable parameters [ 14 ]. Therefore, an identifiability test should be conducted as a sanity check when a new ODE-based mechanistic model is proposed, to ensure trustworthy parameter estimation.…”

Cure and death play a role in understanding dynamics for COVID-19: Data-driven competing risk compartmental models, with and without vaccination

“…For exponential hazards, corresponding to the classical SIR model, parameters were set to Regarding the issue of identifiability and observability, the classical SIR model is structurally identifiable with observable state S(t) when either I(t) or cummulative incidence data is used for the directly measured state [36]. These results continue to hold if the removal rate is a continuous time-varying function (see Model 6 from the S1 Appendix of [37]). Thus the SICD is identifiable with observable state S(t).…”

An Application of the Partially Observed Markov Process in the Analysis of Transmission Dynamics of COVID-19 via Wastewater

“…These models include different states, and differential equations could describe the dynamics of the disease transmission. Since the outbreak of COVID-19 in early 2020, the study of transmission dynamics of COVID-19 [15] is more and more of interest. Because of the incubation period, the number of reported cases of COVID-19 might not reflect the transmission perfectly.…”