Epidemiological measures for informing the general public during the SARS-CoV-2-outbreak: simulation study about bias by incomplete case-detection

During the SARS-CoV-2 outbreak, several epidemiological measures, such as cumulative case-counts, incidence rates, effective reproduction numbers and doubling times, have been used to inform the general public and to justify interventions such as lockdown. During the course of the epidemic, it has been very likely that not all infectious people have been identified, which lead to incomplete case-detection. Apart from asymptomatic infections, possible reasons for incomplete case-detection are availability of test kits and changes in test policies during the course of the epidemic. So far, it has not been examined how biased the reported epidemiological measures are in the presence of incomplete case detection. In this work, we assess the four frequently used measures with respect to incomplete case-detection: 1) cumulative case-count, 2) incidence rate, 3) effective reproduction number and 4) doubling time. We apply an age-structured SIR model to simulate a SARS-CoV-2 outbreak followed by a lockdown in a hypothetical population. Different scenarios about temporal variations in case-detection are applied to the four measures during outbreak and lockdown. The biases resulting from incomplete case-detection on the four measures are compared. It turns out that the most frequently used epidemiological measure, the cumulative case count is most prone to bias in all of our settings. The effective reproduction number is the least biased measure. With a view to future reporting about this or other epidemics, we recommend to use of the effective reproduction number for informing the general public and policy makers.