Abstract
BACKGROUND Public health measures and private behaviour are based on reported numbers of SARS-CoV-2 infections. Some argue that testing influences the confirmed number of infections.
OBJECTIVES/METHODS Do time series on reported infections and the number of tests allow one to draw conclusions about actual infection numbers? A SIR model is presented where the true numbers of susceptible, infectious and removed individuals are unobserved. Testing is also modelled.
RESULTS Official confirmed infection numbers are likely to be biased and cannot be compared over time. The bias occurs because of different reasons for testing (e.g. by symptoms, representative or testing travellers). The paper illustrates the bias and works out the effect of the number of tests on the number of reported cases. The paper also shows that the positive rate (the ratio of positive tests to the total number of tests) is uninformative in the presence of non-representative testing.
CONCLUSIONS A severity index for epidemics is proposed that is comparable over time. This index is based on Covid-19 cases and can be obtained if the reason for testing is known.
Competing Interest Statement
The authors have declared no competing interest.
Funding Statement
no external funding
Author Declarations
I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained.
Yes
The details of the IRB/oversight body that provided approval or exemption for the research described are given below:
no approval or exemption necessary
All necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived.
Yes
I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).
Yes
I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable.
Yes
Data Availability
Descriptive statistics on the number of CoV-2 infections in Germany from RKI and number of SARS-CoV-2 tests from RKI