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Abstract

Two methods of calculating the reproduction index from daily new infection data (incidence) are considered, one by using the generation time Gt 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 (which
s commonly used) is shown to be at variance with the true reproduction index, we fi nd 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, calc RI , which
can be calculated directly from RG . It shows largely the same behaviour as RI
, with less fi ne 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 introduce an entirely new, self-consistent method to derive, an improved corr RI
which is both accurate and contains the details of the epidemic spreading dynamics. Hence we obtain R accurately from incidence data alone. Moreover, plotting
R versus incidence reveals the orbital structure of epidemic waves, whose fi ne structure features clearly correlate with public events and interventions, thus
providing a sensitive diagnostic tool for policy making. It is demonstrated that the widespread use of only incidence as a diagnostic tool is clearly inappropriate.