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

Zhang, Sheng; Ponce, Joan; Zhang, Zhen; Lin, Guang; Karniadakis, George Em

doi:10.1101/2021.02.22.21252255

Cited by 2 publications

(4 citation statements)

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“…We consider the effect of vaccination in models 𝕀 1 , 𝕀 2 , 𝕀 3 , and 𝕋 1 by adding the extra connection from S to R with the rate . Here, V ( t ) denotes the number of effective vaccinated individuals at time t , which is calculated by V ( t ) = 0.52( D 1 ( t ) − D 2 ( t )) + 0.95 D 2 ( t ) 17 . The terms D 1 and D 2 denote the number of individuals that have received the first and second doses of vaccine, respectively.…”

Section: Resultsmentioning

confidence: 99%

“…The identifiability of integer-order models with piece-wise constant parameters has been systematically investigated in 17 . However, such analysis is not available for the fractional models, which may exhibit higher uncertainty; see Fig.…”

Section: Discussionmentioning

confidence: 99%

“…We consider the auxiliary cumulative compartments ( I c and H c ) to help fitting the available data. The three crucial time-dependent parameters are the community transmission rate ( β I ( t )), proportion of disease related death from the H class ( q ( t )), and proportion of hospitalized individuals ( p ( t )), as explained in 17 .…”

Section: Model Pluralitymentioning

confidence: 99%

“…The PINN formulation allows the parameters to be time-dependent functions, represented by separate neural networks, and this makes the inverse problem of inferring the parameters and unobserved dynamics from available data readily applicable to several different models. The structural and practical identifiability of integer-order models have been recently studied in 17 . However, this analysis cannot be applied to the fractional models or even to integer-order models with parameters, which are continuous functions of time.…”

mentioning

confidence: 99%

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Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks

Kharazmi

Cai

Zheng

et al. 2021

Preprint

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We analyze a plurality of epidemiological models through the lens of physics-informed neural networks (PINNs) that enable us to identify multiple time-dependent parameters and to discover new data-driven fractional differential operators. In particular, we consider several variations of the classical susceptible-infectious-removed (SIR) model by introducing more compartments and delay in the dynamics described by integer-order, fractional-order, and time-delay models. We report the results for the spread of COVID-19 in New York City, Rhode Island and Michigan states, and Italy, by simultaneously inferring the unknown parameters and the unobserved dynamics. For integer-order and time-delay models, we fit the available data by identifying time-dependent parameters, which are represented by neural networks (NNs). In contrast, for fractional differential models, we fit the data by determining different time-dependent derivative orders for each compartment, which we represent by NNs. We investigate the identifiability of these unknown functions for different datasets, and quantify the uncertainty associated with NNs and with control measures in forecasting the pandemic.

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Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Model Pluralitymentioning

confidence: 99%

mentioning

confidence: 99%

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Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks

Kharazmi

Cai

Zheng

et al. 2021

Preprint

Self Cite

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Mathematical Modeling of Periodic Outbreaks with Waning Immunity: A Possible Long-Term Description of COVID-19

Viguerie,

Carletti,

Silvestri

et al. 2023

Mathematics

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The COVID-19 pandemic is still ongoing, even if the emergency is over, and we now have enough data to analyze the outbreak over a long timeline. There is evidence that the outbreak alternates periods of high and low infections. Retrospectively, this can help in understanding the nature of an appropriate mathematical model for this dramatic infection. The periodic behavior may be the consequence of time-dependent coefficients related to seasonal effects and specific political actions, or an intrinsic feature of the model. The present paper relies on the assumption that the periodic spikes are an intrinsic feature of the disease, and, as such, it should be properly reflected in the mathematical model. Based on the concept of waning immunity proposed for other pathologies, we introduce a new model with (i) a compartment for weakly immune people subject to immunity booster, represented by a non-linear term; (ii) discrimination between individuals infected/vaccinated for the first time, and individuals already infected/vaccinated, undergoing to new infections/doses. We analyze some preliminary properties of our model, called SIRW2, and provide a proof-of-concept that it is capable of reproducing qualitatively the long-term oscillatory behavior of COVID-19 infection.

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

Cited by 2 publications

References 46 publications

Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks

Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks

Mathematical Modeling of Periodic Outbreaks with Waning Immunity: A Possible Long-Term Description of COVID-19

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