The incidence-based dynamic reproduction index: accurate determination, diagnostic sensitivity, and predictive power

Two methods of calculating the reproduction index from daily new infection data are considered, one by using the generation time t G as a shift (R G ), and an incidence-based method directly derived from the differential equation system of an SIR epidemic dynamics model (R I ). While the former is shown to have few in common with the true reproduction index, we find that the latter provides a sensitive detection device for intervention effects and other events affecting the epidemic, making it well-suited for diagnostic purposes in policy making. Furthermore, we introduce a similar quantity, ![Graphic][1], which can be calculated directly from R G . It shows largely the same behaviour as R I , with less fine structure. However, it is accurate in particular in the vicinity of R = 1, where accuracy is important for the corrrect prediction of epidemic dynamics. We introduce an entirely new, self-consistent method to derive, from both quantities, an improved ![Graphic][2] which is both accurate and contains the details of the epidemic spreading dynamics. Hence we obtain R accurately from data on daily new infections (incidence) alone. Moreover, by using R I instead of R G in plots of R versus incidence, orbital trajectories of epidemic waves become visible in a particularly insightful way, demonstrating that the widespread use of only incidence as a diagniostic tool is clearly inappropriate. PACS numbers: ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This study did not receive any 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: Simulations and evaluations are based on the data source given below. I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. 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 All data are available under "daily reports of the Robert-Koch-Institute / Germany" [1]: /embed/inline-graphic-1.gif [2]: /embed/inline-graphic-2.gif