Fig 6. Sensitivity of β(t) estimation error to data-generating parameters other than 〈β〉 and α.

Plotted in each panel is the median RRMSE (Eq (33)) in estimates of a seasonally forced β(t) (Eq (27)) from simulated reported incidence time series (Δt = 1 week, n = 1042), as a univariate function of each of 5 or 6 data-generating parameters (indicated by the legend). When simulating reported incidence, reference values (Table 1) were assigned to all but the focal parameter, which was assigned 41 values logarithmically spaced between $\frac{1}{4}$ and 4 times its reference value. The horizontal axis (logarithmic scale) measures the ratio of the focal parameter’s true value to its reference value, so that commensurate deviations from the reference case can be compared across parameters. For each parametrization, 1000 simulations were performed with environmental stochasticity [ES] (ϵ = 0.5) and with or without demographic stochasticity [DS] and observation error [OE], as indicated by row: [Row A] without DS or OE (p_rep = 1, t_rep = 0 weeks), [Row B] with DS but without OE (p_rep = 1, t_rep = 0 weeks), or [Row C] with DS and OE (p_rep = 0.25 except when p_rep is the focal parameter, t_rep = 2 weeks). Corresponding mock birth and natural mortality time series were created, then β(t) was estimated from the data using [Left] the S method and [Right] the SI method, all without input error. For each set of estimates of β(t) (1000 estimates per parametrization, per simulation method, per estimation method), the median RRMSE was calculated (after smoothing with fixed q; see Eq (59)) and displayed as one point in the appropriate panel and graph.