Inferring COVID-19 spreading rates and potential change points for case number forecasts

Jonas Dehning; Johannes Zierenberg; Frank Paul Spitzner; Michael Wibral; Joao Pinheiro Neto; Michael Wilczek; Viola Priesemann

As short-term forecasts are time-critical at the onset of an epidemic, the available real-world data is typically not informative enough to identify all free parameters, or to empirically find their underlying distributions. We therefore chose informative priors on initial model parameters where possible and complemented them with uninformative priors otherwise. Our choices are summarized in Tab. III for the simple model, SIR model with stationary spreading rate for the exponential onset phase, and in Tab. IV for the full model with change points, and justified in the following. Priors for the simple model (Table III) : In order to constrain our simple model, an SIR model with stationary spreading rate for the exponential onset phase, we chose the following informative priors. Because of the ambiguity between the spreading and recovery rate in the exponential onset phase (see description of simple model), we chose a narrow log-normal prior for the recovery rate µ ∼ LogNormal(log(1/8), 0.2) with median recovery time of 8 days [20] . Note that, our implementation of µ accounts for the recovery of infected people and isolation measures because it describes the duration during which a person can infect others. For the spreading rate, we assume a broad log-normal prior distribution λ ∼ LogNormal(log(0.4), 0.5) with median 0.4. This way, the prior for λ − µ has median 0.275 and the prior for the base reproduction number (R 0 = λ/µ) has median 3.2, consistent with the broad range of previous estimates [18, 33, 34] . In addition, we chose a log-normal prior for the reporting delay D ∼ LogNormal(log(8), 0.2) to incorporate both the incubation time between 1-14 days with median 5 [32] plus a delay from infected people waiting to contact the doctor and get tested.