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Improved estimation of time-varying reproduction numbers at low case incidence and between epidemic waves

Fig 1

EpiFilter algorithm and relationship to other methods.

In the left panels we consider three ways of inferring the instantaneous or effective reproduction number at time s, R_s, from the incidence curve, (blue dots). The filtering solution produces the posterior distribution p_s from all data prior to time s. EpiEstim approximates this solution by using the subset of data in a window of size k into the past. Reverse-filtering considers the complementary part of the incidence curve, leading to r_s, which utilises data beyond s. The WT method, with future window k, approximates this type of solution. Smoothing uses all information from to generate q_s, which is precisely computed by EpiFilter. Blue windows show the portions of that inform on R_s for each of p_s, r_s and q_s while red windows highlight the subsets used by EpiEstim and the WT method. Double arrows indicate data used for constructing various posterior distributions, while square arrows pinpoint instances of those distributions at the edges of . In the right panels we summarise the construction of EpiFilter. We outline the main assumptions (the model box) and computations (the algorithm box) necessary for realising EpiFilter, which allow us to obtain the most informative and minimum mean squared error (MSE) smoothing posterior distribution q_s. See the main text for the specific equations employed in our implementation [14].

doi: https://doi.org/10.1371/journal.pcbi.1009347.g001