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Fast estimation of time-varying infectious disease transmission rates
Fig 9
Convergence of estimates of S0 obtained using peak-to-peak iteration (PTPI).
S0 was estimated by applying PTPI (25 iterations) to 1000 incidence time series (i.e., 1000 realizations of a reported incidence time series, scaled by 
). An initial guess for S0 was taken to be 
or 4 times the true (data-generating) value. For each initial guess, this process generated 1000 sequences of 26 estimates of S0. Plotted are the median [black lines] and 5th–95th percentile range [grey bands] of the estimate of S0 at each iteration, for the first 10 iterations. The vertical axis measures (on a logarithmic scale) the ratio of the estimated and true values of S0, hence convergence close to 1 [dashed green line] represents convergence of the estimates close to the true value. [Details] One thousand reported incidence time series (Δt = 1 week, n = 1042) were 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, including S0 (hence S0 was the same in all simulations). True incidence was estimated from reported incidence via Eq (26a) (with reporting parameters prep and trep correctly specified), yielding 1000 time series of estimated incidence. Corresponding mock (constant) birth and natural mortality time series were created (with vital rates νc and μc correctly specified), and these data (estimated incidence, births, natural mortality) were passed to the PTPI algorithm, allowing for iterative re-estimation of S0.
doi: https://doi.org/10.1371/journal.pcbi.1008124.g009