An official website of the United States government
Recent outbreaks of Mpox and Ebola, and worrying waves of COVID-19, influenza and respiratory syncytial virus, have all led to a sharp increase in the use of epidemiological models to estimate key epidemiological parameters. The feasibility of this estimation task is known as the practical identifiability (PI) problem. Here, we investigate the PI of eight commonly reported statistics of the classic susceptible–infectious–recovered model using a new measure that shows how much a researcher can expect to learn in a model-based Bayesian analysis of prevalence data. Our findings show that the basic reproductive number and final outbreak size are often poorly identified, with learning exceeding that of individual model parameters only in the early stages of an outbreak. The peak intensity, peak timing and initial growth rate are better identified, being in expectation over 20 times more probable having seen the data by the time the underlying outbreak peaks. We then test PI for a variety of true parameter combinations and find that PI is especially problematic in slow-growing or less-severe outbreaks. These results add to the growing body of literature questioning the reliability of inferences from epidemiological models when limited data are available.
more »
« less
The Structural Identifiability of a Humidity-Driven Epidemiological Model of Influenza Transmission
Influenza epidemics cause considerable morbidity and mortality every year worldwide. Climate-driven epidemiological models are mainstream tools to understand seasonal transmission dynamics and predict future trends of influenza activity, especially in temperate regions. Testing the structural identifiability of these models is a fundamental prerequisite for the model to be applied in practice, by assessing whether the unknown model parameters can be uniquely determined from epidemic data. In this study, we applied a scaling method to analyse the structural identifiability of four types of commonly used humidity-driven epidemiological models. Specifically, we investigated whether the key epidemiological parameters (i.e., infectious period, the average duration of immunity, the average latency period, and the maximum and minimum daily basic reproductive number) can be uniquely determined simultaneously when prevalence data is observable. We found that each model is identifiable when the prevalence of infection is observable. The structural identifiability of these models will lay the foundation for testing practical identifiability in the future using synthetic prevalence data when considering observation noise. In practice, epidemiological models should be examined with caution before using them to estimate model parameters from epidemic data.
more »
« less
- Award ID(s):
- 2229605
- PAR ID:
- 10432865
- Date Published:
- Journal Name:
- Viruses
- Volume:
- 14
- Issue:
- 12
- ISSN:
- 1999-4915
- Page Range / eLocation ID:
- 2795
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Parameter estimation from observable or experimental data is a crucial stage in any modeling study. Identifiability refers to one’s ability to uniquely estimate the model parameters from the available data. Structural unidentifiability in dynamic models, the opposite of identifiability, is associated with the notion of degeneracy where multiple parameter sets produce the same pattern. Therefore, the inverse function of determining the model parameters from the data is not well defined. Degeneracy is not only a mathematical property of models, but it has also been reported in biological experiments. Classical studies on structural unidentifiability focused on the notion that one can at most identify combinations of unidentifiable model parameters. We have identified a different type of structural degeneracy/unidentifiability present in a family of models, which we refer to as the Lambda-Omega (Λ-Ω) models. These are an extension of the classical lambda-omega (λ-ω) models that have been used to model biological systems, and display a richer dynamic behavior and waveforms that range from sinusoidal to square wave to spike like. We show that the Λ-Ω models feature infinitely many parameter sets that produce identical stable oscillations, except possible for a phase shift (reflecting the initial phase). These degenerate parameters are not identifiable combinations of unidentifiable parameters as is the case in structural degeneracy. In fact, reducing the number of model parameters in the Λ-Ω models is minimal in the sense that each one controls a different aspect of the model dynamics and the dynamic complexity of the system would be reduced by reducing the number of parameters. We argue that the family of Λ-Ω models serves as a framework for the systematic investigation of degeneracy and identifiability in dynamic models and for the investigation of the interplay between structural and other forms of unidentifiability resulting on the lack of information from the experimental/observational data.more » « less
-
Differential equation models are crucial to scientific processes across many disciplines, and the values of model parameters are important for analyzing the behaviour of solutions. Identifying these values is known as a parameter estimation, a type of inverse problem, which has applications in areas that include industry, finance and biomedicine. A parameter is called globally identifiable if its value can be uniquely determined from the input and output functions. Checking the global identifiability of model parameters is a useful tool when exploring the well-posedness of a given model. This problem has been intensively studied for ordinary differential equation models, where theory, several efficient algorithms and software packages have been developed. A comprehensive theory for PDEs has hitherto not been developed due to the complexity of initial and boundary conditions. Here, we provide theory and algorithms, based on differential algebra, for testing identifiability of polynomial PDE models. We showcase this approach on PDE models arising in the sciences.more » « less
-
Identifiability of a mathematical model plays a crucial role in the parameterization of the model. In this study, we established the structural identifiability of a susceptible-exposed-infected-recovered (SEIR) model given different combinations of input data and investigated practical identifiability with respect to different observable data, data frequency, and noise distributions. The practical identifiability was explored by both Monte Carlo simulations and a correlation matrix approach. Our results showed that practical identifiability benefits from higher data frequency and data from the peak of an outbreak. The incidence data gave the best practical identifiability results compared to prevalence and cumulative data. In addition, we compared and distinguished the practical identifiability by Monte Carlo simulations and a correlation matrix approach, providing insights into when to use which method for other applications.more » « less
-
The integration of viral genomic data into public health surveillance has revolutionized our ability to track and forecast infectious disease dynamics. This review addresses two critical aspects of infectious disease forecasting and monitoring: the methodological workflow for epidemic forecasting and the transformative role of molecular surveillance. We first present a detailed approach for validating epidemic models, emphasizing an iterative workflow that utilizes ordinary differential equation (ODE)-based models to investigate and forecast disease dynamics. We recommend a more structured approach to model validation, systematically addressing key stages such as model calibration, assessment of structural and practical parameter identifiability, and effective uncertainty propagation in forecasts. Furthermore, we underscore the importance of incorporating multiple data streams by applying both simulated and real epidemiological data from the COVID-19 pandemic to produce more reliable forecasts with quantified uncertainty. Additionally, we emphasize the pivotal role of viral genomic data in tracking transmission dynamics and pathogen evolution. By leveraging advanced computational tools such as Bayesian phylogenetics and phylodynamics, researchers can more accurately estimate transmission clusters and reconstruct outbreak histories, thereby improving data-driven modeling and forecasting and informing targeted public health interventions. Finally, we discuss the transformative potential of integrating molecular epidemiology with mathematical modeling to complement and enhance epidemic forecasting and optimize public health strategies.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/v14122795
