Projecting the Spread of COVID19 for Germany

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 effects of public regulations. For all scenarios we report the expected end of the CoV-2 epidemic.

We have four general findings: First, current epidemiological thinking implies that the long-run effects 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 influence the dynamics of spread of CoV-2. Second, predictions about the duration and level of the epidemic must strongly distinguish between the officially 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 offer 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.

Concerning predictions about COVID-19 in Germany, we find that the long-run number of sick individuals (that are reported to the RKI), once the epidemic is over, will lie between 500 thousand and 5 million individuals. While this seems to be an absurd large range for a precise projection, this reflects 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.

Defining the end of the epidemic by less than 100 newly reported sick individuals per day, we find a large variation depending on the effectiveness of governmental pleas and regulations to reduce social contacts. An epidemic that is not influenced by public health measures would end mid June 2020. With public health measures lasting for few weeks, the end is delayed by around one month or two. The advantage of the delay, however, is to reduce the peak number of individuals that are simultaneously sick. When we believe in long-run infection rates of 70%, this number is equally high for all scenarios we went through and well above 1 million. When we can hope for the Hubei-scenario, the maximum number of sick individuals will be around 200 thousand “only”.

Whatever value of the range of long-run infection rates we want to assume, the epidemic will last at least until June, with extensive and potentially future public health measures, it will last until July. In the worst case, it will last until end of August.

We emphasize that all projections are subject to uncertainty and permanent monitoring of observed incidences are taken into account to update the projection. The most recent projections are available at<ext-link xmlns:xlink="http://www.w3.org/1999/xlink" ext-link-type="uri" xlink:href="https://www.macro.economics.unimainz.de/corona-blog/">https://www.macro.economics.unimainz.de/corona-blog/</ext-link>.