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.

SUTRA: A Novel Approach to Modelling Pandemics with Applications to COVID-19

“…Book length treatments are available in [2,8,14,6,20]. According to [21], there are no fewer than thirty six epidemiological models. Historically the first epidemiological model is the SIR model introduced in [15], given by Ṡ = −βIS, İ = βIS − γI, Ṙ = γI,…”

A Dynamical Framework for Modeling Fear of Infection and Frustration with Social Distancing in COVID-19 Spread

“…This is positive, so that all the first-column entries of the Routh-Hurwitz table are positive. It follows that all of the eigenvalues of (15) have negative real part so that the endemic steady state of ( 17) is locally asymptotically stable. It follows that the system with one delay is not consistent with sustained oscillations around the endemic steady state (18).…”

“…Studies have estimated the basic reproductive number, a key measure of the transmissibility of a disease, of SARS-CoV-2 [2,3,4,5] and projected the disease's spread under a wide variety of public policy intervention scenarios, including variances in social distancing policies, travel restrictions, and face mask utilization [6,7,8,9,10,11]. Forecasting the extent of the spread of COVID-19, however, has been complicated by many factors, including evidence of asymptomatic spread [12,13], issues with parameter identifiability [14,15], and the uncertain mechanisms by which social behaviors have altered the spread of the disease to date [16,17,18].…”

Lack of practical identifiability may hamper reliable predictions in COVID-19 epidemic models

“…In the context of epidemics forecasting, this means that even if the model considered is able to reproduce the measured variables, a large uncertainty may affect the estimated values of the parameters and the predicted evolution of the unmeasured variables [22]. Although the problem of structural identifiability has been investigated already for a large number of COVID-19 epidemic models [23], the more subtle problem of the practical identifiability of such models has not been faced yet. Moreover, in the few existing studies on the practical identifiability of epidemiological models, only the sensitivity of measured variables to the parameters of the model has been considered, and mainly through numerical simulations [24,25].…”