Fast estimation of time-varying infectious disease transmission rates
Fig 4
Reduction in β(t) estimation error with optimal loess smoothing.
The horizontal axis measures the case reporting probability prep, for which 41 values equally spaced on a logarithmic scale between 0.01 and 1 were considered. Using each value of prep and reference values (Table 1) for all other parameters, 100 reported incidence time series (Δt = 1 week, n = 1042) were simulated accounting for environmental noise in transmission (ϵ = 0.5), demographic stochasticity, and random under-reporting of cases (measured by prep). The underlying seasonally forced β(t) (Eq (27)) was estimated from reported incidence using the S and SI methods, both applied without input error, yielding two raw estimates βk per simulation. Smooth loess curves βloess(t; q) (q = 10, …, 110; cf. §2.2.6) were fit to each βk time series. The optimal q for a given time series, denoted by qopt, was defined as the value that minimized RRMSE (Eq (33)) in βloess(tk; q). Overall, for each value of prep and each β(t) estimation method (S and SI), 100 values of qopt were obtained corresponding to 100 βk time series. Plotted on the vertical axis as functions of prep are the median and 5th and 95th percentiles of [Panel A] RRMSE in the raw estimates βk [dashed lines] and optimal loess estimates βloess(tk; qopt) [solid lines] and [Panel B] qopt. Lines and bands indicate the median and 5th–95th percentile range, respectively. Results for the S and SI methods are shown in green and red, respectively.