Fast estimation of time-varying infectious disease transmission rates
Fig 3
Bias and variance in 1-year cycles embedded in three estimates of a seasonally forced β(t).
[Panel A] In black, the seasonally forced β(t) (Eq (27)) underlying 1000 years of simulated reported incidence data. In (transparent) colour, raw estimates βk obtained from the data by the S [green] and SI [red] methods, both applied without input error. Only the first 10 of 1000 years are shown. [Panels B and C] In black, the true 1-year cycle in the seasonally forced β(t). In light (transparent) colour, the 1000 1-year cycles embedded in the linear interpolant βint(t) of βk. In dark colour, the average 1-year cycle (Eq (22a)) in βint(t). Results are shown for both the S [Panel B, green] and SI [Panel C, red] methods. [Panel D] Like Panel C, except for a smooth loess curve βloess(t; q) (q = 53) fit to βk, instead of the interpolant βint(t). [Details] A reported incidence time series with 1000 years of weekly observations (Δt = 1 week, n = 52153) was simulated with environmental noise in transmission (ϵ = 0.5), demographic stochasticity, and random under-reporting of cases (prep = 0.25), using reference values (Table 1) for the remaining parameters.