Optimising Renewal Models for Real-Time Epidemic Prediction and Estimation

KV Parag; CA Donnelly

The time-series of infected cases (infecteds) observed over the course of an in-are provided in the Methods. The APE uses the window of data preceding time 126 s, (I s s−k+1 , Λ s s−k+1 ), to predict the incidence at s + 1 and assigns a log-score to 127 this prediction. This procedure is repeated over s ≤ t and for possible k-values. 128 The k achieving the minimum cumulated log-score is deemed optimal. Fig. 1 129 illustrates the APE for selecting between two windows k 1 and k 2 . Figure 1 : Window length selection using APE. An observed incidence curve (blue dots) is sequentially and causally predicted over time s ≤ t, using effective reproduction number estimates based on two possible windows lengths of k 1 and k 2 (green shaded). The true reproduction number (R s ) is drawn in dashed black (inset). Its estimates for each window length areR τ1(s) (dark grey) andR τ2(s) (light grey). Large windows (k 1 ) smooth over fluctuations. Small ones (k 2 ) recover these changes but are noisy. The APE assesses k 1 and k 2 via the log-loss of their sequential predictions (red error bars shown for predictions at t 1 and t 2 under k 1 and k 2 respectively). The k-window with the smaller APE is better supported by this incidence curve. The algorithm parameters are defined in Results.