Global Identifiability of Differential Models

Ponce

et al. 2021

Preprint

Epidemiological models can provide the dynamic evolution of a pandemic but they are based on many assumptions and parameters that have to be adjusted over the time when the pandemic lasts. However, often the available data are not sufficient to identify the model parameters and hence infer the unobserved dynamics. Here, we develop a general framework for building a trustworthy data-driven epidemiological model, consisting of a workflow that integrates data acquisition and event timeline, model development, identifiability analysis, sensitivity analysis, model calibration, model robustness analysis, and forecasting with uncertainties in different scenarios. In particular, we apply this framework to propose a modified susceptible-exposed-infectious-recovered (SEIR) model, including new compartments and model vaccination in order to forecast the transmission dynamics of COVID-19 in New York City (NYC). We find that we can uniquely estimate the model parameters and accurately predict the daily new infection cases, hospitalizations, and deaths, in agreement with the available data from NYC's government's website. In addition, we employ the calibrated data-driven model to study the effects of vaccination and timing of reopening indoor dining in NYC.

Section: Structural Identifiabilitymentioning

confidence: 99%

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

Ponce

et al. 2021

Preprint

“…Scenarios 1 and 2 require that only a single initial condition holds a nonzero value. The first scenario is associated with the measured sensor in (19). In the third, a set of 3 specific nonzero initial conditions is defined.…”

Section: /16mentioning

confidence: 99%

“…The local structural identifiability of 6 of the 7 system parameters α 1 , k a ,V m , k c , β 1 and β 2 , could be confirmed with the Taylor series method. In a recent publication 19 , the global identifiability result of Saccomani et. al.…”

Section: Example 5 Pharmacokinetics Model (M 5 )mentioning

confidence: 99%

Assessing the Role of Initial Conditions in the Local Structural Identifiability of Large Dynamic Models

Joubert

Stigter

Molenaar

2021

Preprint

Structural identifiability is a binary property that determines whether or not unique parameter values can, in principle, be estimated from error-free input-output data. The many papers that have been written on this topic collectively stress theimportance of this a priori analysis in the model development process. The story however, often ends with a structurallyunidentifiable model. This may leave a model developer with no plan of action on how to address this potential issue. We continue this model exploration journey by identifying one of the possible sources of a model’s unidentifiability: problematic initial conditions. It is well-known that certain initial values may result in the loss of local structural identifiability. Nevertheless, literature on this topic has been limited to the analysis of small toy models. Here, we present a systematic approach to detect problematic initial conditions of real-world systems biology models, that are usually not small. A model’s identifiability can often be reinstated by changing the value of such problematic initial conditions. This provides modellers an option to resolve the “unidentifiablemodel” problem. Additionally, a good understanding of which initial values should rather be avoided can be very useful during experimental design. We show how our approach works in practice by applying it to five models. First, two small benchmark models are studied toget the reader acquainted with the method. The first one shows the effect of a zero-valued problematic initial condition. The second one illustrates that the approach also yields correct results in the presence of input signals and that problematic initial conditions need not be zero-values. For the remaining three examples, we set out to identify key initial values which may result in the structural unidentifiability. The third and fourth examples involve a systems biology Epo receptor model and a JAK/STAT model, respectively. In the final Pharmacokinetics model, of which its global structural identifiability has only recently been confirmed, we indicate that there are still sets of initial values for which this property does not hold.

Annual Reviews in Control

“…It is written in Maple and available at https://github.com/pogudingleb/SIAN. The paper [46] gives the theoretical foundations of this algorithm. Finally, the paper [57] describes a Mathematica implementation of the probabilistic semi-numerical algorithm described in [42].…”

Section: Output Equalitymentioning

confidence: 99%

“…θ(3) y k+1 − y k+3 + m k+2 + θ (2) θ (4) m k+1 = 0 θ (1) y 2 k+3 + θ (2) θ (3) y k+2 − y k+4 + m k+3 + θ (2) θ (4) m k+2 = 0 θ (1) y 2 k+4 + θ (2) θ (3) y k+3 − y k+5 + m k+4 + θ (2) θ (4) m k+3 = 0(46) …”

mentioning

confidence: 99%

A priori identifiability: An overview on definitions and approaches

Anstett-Collin

Denis-Vidal

Millérioux

2020

For a system, a priori identifiability is a theoretical property depending only on the model and guarantees that its parameters can be uniquely determined from observations. This paper provides a survey of the various and numerous definitions of a priori identifiability given in the literature, for both deterministic continuous and discrete-time models. A classification is done by distinguishing analytical and algebraic definitions as well as local and global ones. Moreover, this paper provides an overview on the distinct methods to test the parameter identifiability. They are classified into the so-called output equality approaches, local state isomorphism approaches and differential algebra approaches. A few examples are detailed to illustrate the methods and complete this survey.