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Non-parametric model-based estimation of the effective reproduction number for SARS-CoV-2

Viral outbreaks, such as the current COVID-19 pandemic, are commonly described by compartmental models by means of ordinary differential equation (ODE) systems. The parameter values of these ODE models are typically unknown and need to be estimated based on accessible data. In order to describe realistic pandemic scenarios with strongly varying situations, these model parameters need to be assumed as time-dependent. While parameter estimation for the typical case of time-constant parameters does not pose larger issues, the determination of time-dependent parameters, e.g.~the transition rates of compartmental models, remains notoriously difficult, in particular since the function class of these time-dependent parameters is unknown. In this work, we present a novel method which utilizes the Augmented Kalman Smoother in combination with an Expectation-Maximization algorithm to simultaneously estimate all time-dependent parameters in an SIRD compartmental model. This approach only requires incidence data, but no prior knowledge on model parameters or any further assumptions on the function class of the time-dependencies. In contrast to other approaches for the estimation of the time-dependent reproduction number, no assumptions on the parameterization of the serial interval distribution are required. With this method, we are able to adequately describe COVID-19 data in Germany and to give non-parametric model-based time course estimates for the effective reproduction number.

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