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

In order to quantify the impact of possible interventions, we concentrate on the effective growth of active infections before and after the intervention. As long as the number of infections and recoveries are small compared to the population size, the number of active infections per day can be approximated by an exponential growth (Fig. 1A ,B) with effective growth rate λ * = λ − µ (see Methods). As a consequence, λ and µ cannot be estimated independently. This is further supported by a systematic scan of the model's log-likelihood in the λ-µ space that shows an equipotential line for the maximum likelihood ( Fig. 1 J) . This strongly suggests that the growth rate λ * is the relevant free parameter with a median λ * = 28% (Fig. 1 I) . The control parameter of the dynamics in the exponential phase is thus the (effective) growth rate: If the growth rate is larger than zero (λ > µ), case numbers grow exponentially; if the growth rate is smaller than zero (λ < µ), the recovery dominates and the new confirmed cases decrease. The two different dynamics (supercritical and subcritical, respectively) are separated by a critical point at λ * = 0 (λ = µ) [36] .