Fig. 1

We simulated a directly transmitted immunizing pathogen with 50 varying intensities of seasonal transmission and then determined if signatures of critical slowing down were detectable. In all simulations, average R ₀ (i.e., the number of secondary infected cases arising from a single infected case in an entirely susceptible population) increases linearly after year 10 (t ₁₀) and fluctuates seasonally according to the amplitude of seasonality, β ₁. From left to right, β ₁ is equal to 0, 0.019, 0.04 and β ₀=0.04/ day. The amplitude relative to baseline transmission (referred to here as relative fluctuation) are equal to 0, 0.49, and 1. Values of other parameters are given in Table 2. In the top two rows, a grey dashed line divides the time series into its null (left of the grey line) and test (right of the grey line) intervals used for calculating reliability of each early warning statistic. The bottom row shows the wavelet power spectrum of the simulated data (middle row) with time along the x-axis and frequency along the y-axis. Lower frequencies correspond to longer periods (i.e., the bottom of the spectrum) and higher frequencies correspond to lower periods (i.e., the top of the spectrum). The colors code for power coefficients from dark blue, low values (0), to dark red, high values (1·10⁵). High wavelet coefficients indicate which frequencies are more powerful at that point in time