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, , 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 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: