OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany

Mathematical models in epidemiology are an indispensable tool to determine the dynamics and important characteristics of infectious diseases. Apart from their scientific merit, these models are often used to inform political decisions and interventional measures during an ongoing outbreak. However,...

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Autores principales:	Stefan T. Radev, Frederik Graw, Simiao Chen, Nico T. Mutters, Vanessa M. Eichel, Till Bärnighausen, Ullrich Köthe
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Biology (General) QH301-705.5
Acceso en línea:	https://doaj.org/article/700dce7161f14b92b9338f3773914f5d
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spelling	oai:doaj.org-article:700dce7161f14b92b9338f3773914f5d2021-11-18T05:51:58ZOutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany1553-734X1553-7358https://doaj.org/article/700dce7161f14b92b9338f3773914f5d2021-10-01T00:00:00Zhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC8584772/?tool=EBIhttps://doaj.org/toc/1553-734Xhttps://doaj.org/toc/1553-7358Mathematical models in epidemiology are an indispensable tool to determine the dynamics and important characteristics of infectious diseases. Apart from their scientific merit, these models are often used to inform political decisions and interventional measures during an ongoing outbreak. However, reliably inferring the epidemical dynamics by connecting complex models to real data is still hard and requires either laborious manual parameter fitting or expensive optimization methods which have to be repeated from scratch for every application of a given model. In this work, we address this problem with a novel combination of epidemiological modeling with specialized neural networks. Our approach entails two computational phases: In an initial training phase, a mathematical model describing the epidemic is used as a coach for a neural network, which acquires global knowledge about the full range of possible disease dynamics. In the subsequent inference phase, the trained neural network processes the observed data of an actual outbreak and infers the parameters of the model in order to realistically reproduce the observed dynamics and reliably predict future progression. With its flexible framework, our simulation-based approach is applicable to a variety of epidemiological models. Moreover, since our method is fully Bayesian, it is designed to incorporate all available prior knowledge about plausible parameter values and returns complete joint posterior distributions over these parameters. Application of our method to the early Covid-19 outbreak phase in Germany demonstrates that we are able to obtain reliable probabilistic estimates for important disease characteristics, such as generation time, fraction of undetected infections, likelihood of transmission before symptom onset, and reporting delays using a very moderate amount of real-world observations. Author summary Emerging infections and epidemic outbreaks are associated with large uncertainties concerning data integrity that challenge the timely detection of disease characteristics and dynamics. Robust parameter inference for mathematical models aiming to describe these dynamics is essential to predict the progression of an epidemic and inform on appropriate public health interventions. In this study, we present a novel method based on invertible neural networks that allows inference of important epidemiological characteristics in case of limited data, thereby allowing for reliable uncertainty quantification. The method circumvents common challenges associated with sparse data by using simulation-based training of an expressive generative neural network. Applying our method to data of the early Covid-19 epidemic in Germany, we are able to obtain reliable estimates on important disease characteristics, such as the proportion of infected individuals remaining undetected, despite limited observations during early outbreak dynamics.Stefan T. RadevFrederik GrawSimiao ChenNico T. MuttersVanessa M. EichelTill BärnighausenUllrich KöthePublic Library of Science (PLoS)articleBiology (General)QH301-705.5ENPLoS Computational Biology, Vol 17, Iss 10 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Biology (General) QH301-705.5
spellingShingle	Biology (General) QH301-705.5 Stefan T. Radev Frederik Graw Simiao Chen Nico T. Mutters Vanessa M. Eichel Till Bärnighausen Ullrich Köthe OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany
description	Mathematical models in epidemiology are an indispensable tool to determine the dynamics and important characteristics of infectious diseases. Apart from their scientific merit, these models are often used to inform political decisions and interventional measures during an ongoing outbreak. However, reliably inferring the epidemical dynamics by connecting complex models to real data is still hard and requires either laborious manual parameter fitting or expensive optimization methods which have to be repeated from scratch for every application of a given model. In this work, we address this problem with a novel combination of epidemiological modeling with specialized neural networks. Our approach entails two computational phases: In an initial training phase, a mathematical model describing the epidemic is used as a coach for a neural network, which acquires global knowledge about the full range of possible disease dynamics. In the subsequent inference phase, the trained neural network processes the observed data of an actual outbreak and infers the parameters of the model in order to realistically reproduce the observed dynamics and reliably predict future progression. With its flexible framework, our simulation-based approach is applicable to a variety of epidemiological models. Moreover, since our method is fully Bayesian, it is designed to incorporate all available prior knowledge about plausible parameter values and returns complete joint posterior distributions over these parameters. Application of our method to the early Covid-19 outbreak phase in Germany demonstrates that we are able to obtain reliable probabilistic estimates for important disease characteristics, such as generation time, fraction of undetected infections, likelihood of transmission before symptom onset, and reporting delays using a very moderate amount of real-world observations. Author summary Emerging infections and epidemic outbreaks are associated with large uncertainties concerning data integrity that challenge the timely detection of disease characteristics and dynamics. Robust parameter inference for mathematical models aiming to describe these dynamics is essential to predict the progression of an epidemic and inform on appropriate public health interventions. In this study, we present a novel method based on invertible neural networks that allows inference of important epidemiological characteristics in case of limited data, thereby allowing for reliable uncertainty quantification. The method circumvents common challenges associated with sparse data by using simulation-based training of an expressive generative neural network. Applying our method to data of the early Covid-19 epidemic in Germany, we are able to obtain reliable estimates on important disease characteristics, such as the proportion of infected individuals remaining undetected, despite limited observations during early outbreak dynamics.
format	article
author	Stefan T. Radev Frederik Graw Simiao Chen Nico T. Mutters Vanessa M. Eichel Till Bärnighausen Ullrich Köthe
author_facet	Stefan T. Radev Frederik Graw Simiao Chen Nico T. Mutters Vanessa M. Eichel Till Bärnighausen Ullrich Köthe
author_sort	Stefan T. Radev
title	OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany
title_short	OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany
title_full	OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany
title_fullStr	OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany
title_full_unstemmed	OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany
title_sort	outbreakflow: model-based bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the covid-19 pandemics in germany
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/700dce7161f14b92b9338f3773914f5d
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OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany

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