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Fast estimation of time-varying infectious disease transmission rates

Fig 8

Example of S(t) and β(t) reconstruction with an overestimate of S₀ corrected by peak-to-peak iteration (PTPI).

[Panel A] Truncation step of PTPI (Box 5). Plotted is a reconstruction of true incidence Z(t) from a simulated reported incidence time series, before [Z_k, black] and after [, yellow] smoothing with a 13-point central moving average. Vertical lines indicate peaks in . The times of the first peak in and the last peak occurring at the same phase of the cycle (in this case, the last peak) are denoted by t_a and t_b. [Panel B] Iteration step of PTPI (Box 6), where the initial estimates of both S₀ = S(0) and S(t_a) were taken to be 4 times the true (data-generating) value of S₀. Plotted in grey are successive reconstructions of S(t) between times t_a and t_b, generated by updating the estimate of S(t_a) with the estimate of S(t_b) obtained in the previous iteration. Dashed continuations to the left of t_a display estimation of S₀ backwards in time from estimates of S(t_a). Plotted in black is the result of reconstructing S(t) starting from the final estimate of S₀, which was obtained after 25 iterations and had a relative error of roughly 1.4% (compared to 300% in the initial estimate). [Panel C] The sequence of reconstructions of β(t) corresponding to the estimates of S₀ shown in Panel B. [Details] Twenty years of weekly reported incidence (Δt = 1 week, n = 1042) were simulated with environmental noise in transmission (ϵ = 0.5), demographic stochasticity, and random under-reporting of cases (p_rep = 0.25), using reference values (Table 1) for the remaining parameters. Z(t), S(t) and β(t) were reconstructed from reported incidence using the SI method without input error (apart from mis-specification of S₀).

doi: https://doi.org/10.1371/journal.pcbi.1008124.g008