ZusammenfassungDie Autoren erklären den bisherigen Verlauf von Covid-19 in Deutschland durch Regressionsanalysen und epidemiologische Modelle. Sie beschreiben und quantifizieren den Effekt der gesundheitspolitischen Maßnahmen (GPM), die bis zum 19. April in Kraft waren. Sie berechnen den erwarteten Verlauf der Covid-19-Epidemie in Deutschland, wenn es diese Maßnahmen nicht gegeben hätte, und zeigen, dass die GPM einen erheblichen Beitrag zur Reduktion der Infektionszahlen geleistet haben. Die seit 20. April gelockerten GPM sind zwischen den Bundesländern relativ heterogen, was ein Glücksfall für die Wissenschaft ist. Mittels einer Analyse dieser Heterogenität kann aufgedeckt werden, welche Maßnahmen für eine Bekämpfung einer eventuellen zweiten Infektionswelle besonders hilfreich und besonders schädlich sind.

AbstractWe model the evolution of the number of individuals reported sick with COVID-19 in Germany. Our theoretical framework builds on a continuous time Markov chain with four states: healthy without infection, sick, healthy after recovery or despite infection but without symptoms, and deceased. Our quantitative solution matches the number of sick individuals up to the most recent observation and ends with a share of sick individuals following from infection rates and sickness probabilities. We employ this framework to study inter alia the expected peak of the number of sick individuals in Germany in a scenario without public regulation of social contacts. We also study the effects of public regulations. For all scenarios we report the expected end date of the CoV-2 epidemic.

Many countries consider the lifting of restrictions of social contacts (RSC). We quantify the e¤ects of RSC for Germany. We initially employ a purely statistical approach to predicting prevalence of COVID19 if RSC were upheld after April 20. We employ these …ndings and feed them into our theoretical model. We …nd that the peak of the number of sick individuals would be reached already mid April. The number of sick individuals would fall below 1,000 at the beginning of July. When restrictions are lifted completely on April 20, the number of sick should rise quickly again from around April 27. A balance between economic and individual costs of RSC and public health objectives consists in lifting RSC for activities that have high economic bene…ts but low health costs. In the absence of large-scale representative testing of CoV-2 infections, these activities can most easily be identi…ed if federal states of Germany adopted exit strategies that di¤er across states. . We are grateful to Claudius Gros, Albrecht Ritschl, Hilmar Schneider, Hans-Werner Sinn, to many members of the "Makrorunde"and to seminar participants of the 'Forecasting COVID19' workshop at the Johannes Gutenberg University for comments and discussions.

We model the evolution of the number of individuals that are reported to be sick with COVID-19 in Germany. Our theoretical framework builds on a continuous time Markov chain with four states: healthy without infection, sick, healthy after recovery or after infection but without symptoms and dead. Our quantitative solution matches the number of sick individuals up to the most recent observation and ends with a share of sick individuals following from infection rates and sickness probabilities. We employ this framework to study inter alia the expected peak of the number of sick individuals in a scenario without public regulation of social contacts. We also study the e¤ects of public regulations. For all scenarios we report the expected end of the CoV-2 epidemic.We have four general …ndings: First, current epidemiological thinking implies that the long-run e¤ects of the epidemic only depend on the aggregate long-run infection rate and on the individual risk to turn sick after an infection. Any measures by individuals and the public therefore only in ‡uence the dynamics of spread of CoV-2. Second, predictions about the duration and level of the epidemic must strongly distinguish between the o¢ cially reported numbers (Robert Koch Institut, RKI) and actual numbers of sick individuals. Third, given the current (scarce) medical knowledge about long-run infection rate and individual risks to turn sick, any prediction on the length (duration in months) and strength (e.g. maximum numbers of sick individuals on a given day) is subject to a lot of uncertainty. Our predictions therefore o¤er robustness analyses that provide ranges on how long the epidemic will last and how strong it will be. Fourth, public interventions that are already in place and that are being discussed can lead to more and less severe outcomes of the epidemic. If an intervention takes place too early, the epidemic can actually be stronger than with an intervention that starts later. Interventions should therefore be contingent on current infection rates in regions or countries. of the modelling initiative of the Deutsche Gesellschaft für Epidemiologie for comments and discussions. We are deeply indebted to Damir Stijepic for the initial numerical solutions and the initial calibration. Our biggest debt of gratitude is owed to Matthias Birkner who has been advising and teaching us on stochastic models for many years. : medRxiv preprint over, will lie between 500 thousand and 5 million individuals. While this seems to be an absurd large range for a precise projection, this re ‡ects the uncertainty about the long-run infection rate in Germany. If we assume that Germany will follow the good scenario of Hubei (and we are even a bit more conservative given discussions about data quality), we will end up with 500 thousand sick individuals over the entire epidemic. If by contrast we believe (as many argue) that once the epidemic is over 70% of the population will have been infected (and thereby immune), we will end up at 5 million cases.De…ning the end of the epi...

Background Various forms of contact restrictions have been adopted in response to the Covid-19 pandemic. Around February 2021, rapid testing appeared as a new policy instrument. Some claim it may serve as a substitute for contact restrictions. We study the strength of this argument by evaluating the effects of a unique policy experiment: In March and April 2021, the city of Tübingen set up a testing scheme while relaxing contact restrictions. Methods We compare case rates in Tübingen county to an appropriately identified control unit. We employ the synthetic control method. We base interpretations of our findings on an extended SEIR model. Findings The experiment led to an increase in the reported case rate. This increase is robust across alternative statistical specifications. This is also due to more testing leading initially to more reported cases. An epidemiological model that corrects for ‘more cases due to more testing’ and ‘reduced testing and reporting during the Easter holiday’ confirms that the overall effect of the experiment led to more infections. Interpretation The number of rapid tests were not sufficiently high in this experiment to compensate for more contacts and thereby infections caused by relaxing contact restrictions.