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

Our change point detection builds on a generalization of the simple SIR model with stationary spreading rate. Instead, we now assume that the spreading rate λ i , i = 1, ..., n, may change at certain time points t i from λ i−1 to λ i , linearly over a time window of ∆t i days. Thereby, we account for policy changes to reduce λ, which were implemented in Germany step by step. Thus, the parameters t i , ∆t i , and λ i are added to the parameter set of the simple model above, and the differential equations are augmented by the time-varying λ i . We estimate the set of model parameters θ = {λ i , t i , µ, D, σ, I 0 } using Bayesian inference with Markov-chain Monte-Carlo (MCMC). The parameter σ is the scale factor for the width of the likelihood P Ĉ t θ between observed data and model (see below). Our implementation relies on the python package pymc3 [42] with NUTS (No-U-Turn Sampling) [43] . The structure of our approach is the following: