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

Iteratively update the parameters using MCMC. The drawing of new candidate parameters and the time integration of the SIR model is repeated in every MCMC step. The idea is to probabilistically draw parameter updates and to accept them such that the deviation between the model outcome and the available real-world time-series is likely to reduce. We quantify the inverse deviation (which needs to be maximized) between the model outcome for one time point t, C t (θ) and the corresponding real-world data pointĈ t with the local likelihood by the demographic noise of typical mean-field solutions for epidemic spreading, e.g.,ρ(t) = aρ(t) − bρ 2 (t) + ρ(t)η(t), where ρ is the activity and η(t) is Gaussian white noise [35, 36] . This choice is consistent with our data (Fig. 1 A-C) . The overall deviation is then simply the product of local likelihoods over all time points.