The dynamic reproduction index: accurate determination from incidence and application for an early warning system

Abstract

Two methods of calculating the reproduction index from daily new infection data are considered, one by using the generation time tG as a shift ( RG), and an incidence-based method directly derived from the differential equation system of an SIR epidemic dynamics model (RI). 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, RIcalc, which can be calculated directly from RG. It shows largely the same behaviour as RI, with less fine structure. However, it is accurate in particular in the vicinity of R=1, where accuracy is important for the correct prediction of epidemic dynamics. We show how to obtain an improved RIcorr from both quantities, which is both accurate and contains the details of the epidemic spreading dynamics. Hence we obtain R accurately only from data on daily new infections (incidence). Moreover, by using RI instead of RG in plots ''R versus Incidence'' suddenly expressed trajectories of epidemic wave(s) become visible in a particularly insightful way. In addition this shows that the widespread use of only incidence as a diagnostic tool is clearly inappropriate.