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Mathematical models in epidemiology are an indispensable tool to determinethe dynamics and important characteristics of infectious diseases. Apart fromtheir scientific merit, these models are often used to inform politicaldecisions and intervention measures during an ongoing outbreak. However,reliably inferring the dynamics of ongoing outbreaks by connecting complexmodels to real data is still hard and requires either laborious manualparameter fitting or expensive optimization methods which have to be repeatedfrom scratch for every application of a given model. In this work, we addressthis problem with a novel combination of epidemiological modeling withspecialized neural networks. Our approach entails two computational phases: Inan initial training phase, a mathematical model describing the epidemic is usedas a coach for a neural network, which acquires global knowledge about the fullrange of possible disease dynamics. In the subsequent inference phase, thetrained neural network processes the observed data of an actual outbreak andinfers the parameters of the model in order to realistically reproduce theobserved dynamics and reliably predict future progression. With its flexibleframework, our simulation-based approach is applicable to a variety ofepidemiological models. Moreover, since our method is fully Bayesian, it isdesigned to incorporate all available prior knowledge about plausible parametervalues and returns complete joint posterior distributions over theseparameters. Application of our method to the early Covid-19 outbreak phase inGermany demonstrates that we are able to obtain reliable probabilisticestimates for important disease characteristics, such as generation time,fraction of undetected infections, likelihood of transmission before symptomonset, and reporting delays using a very moderate amount of real-worldobservations.

plos computational biology/plos computational biology

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