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 ( <monospace>R</monospace> _G ), and an incidence-based method directly derived from the differential equation system of an SIR epidemic dynamics model ( <monospace>R</monospace> _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, <inline-formula> <alternatives> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22273599v1_inline1.gif"/> </alternatives> </inline-formula> , which can be calculated directly from <monospace>R</monospace> _G . It shows largely the same behaviour as <monospace>R</monospace> _I , with less fine structure. However, it is accurate in particular in the vicinity of <monospace>R</monospace> = 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 <inline-formula> <alternatives> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22273599v1_inline2.gif"/> </alternatives> </inline-formula> which is both accurate and contains the details of the epidemic spreading dynamics. Hence we obtain <monospace>R</monospace> accurately from data on daily new infections (incidence) alone. Moreover, by using <monospace>R</monospace> _I instead of <monospace>R</monospace> _G in plots of <monospace>R</monospace> 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.

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