Multiple waves

Methodology

This method uses the seasonal onset and burden level methodology to estimate multiple waves for diseases that do not follow a one peak per season pattern. The burden levels are used to define when the first wave has ended by dropping below the desired intensity breakpoint, whereafter a new wave can start. The seasonal onset method is used to determine each wave onset - in the same way as for the single seasonal onset.

The combined_seasonal_output() function implements this functionality by defining the following variables:

• \(\text{multiple_waves}\): A logical. Should the output contain multiple waves?
• \(\text{burden_level_decrease}\): A character string specifying the burden breakpoint the observations should decrease below before a new increase in observations can call a new wave onset if seasonal onset criteria are met. Choose between; “very low”, “low”, “medium”, or “high”.
• \(\text{steps_with_decrease}\): An integer specifying how many time steps (days, weeks, months) the decrease should be observed under the burden_level_decrease before starting the search for a new wave onset.

Applying the multiple waves algorithm

As an example we first generate cases in a tsd object, with the generate_seasonal_data() function. Then we rescale time from monthly to weekly observations to get multiple waves.

set.seed(222)
tsd_data_monthly <- generate_seasonal_data(
  years = 14,
  phase = 3,
  start_date = as.Date("2020-05-18"),
  noise_overdispersion = 5,
  time_interval = "months"
)

tsd_data <- to_time_series(
  cases = tsd_data_monthly$cases,
  time = seq.Date(
    from = as.Date("2020-05-18"),
    by = "week",
    length.out = length(tsd_data_monthly$cases)
  )
) |>
  dplyr::filter(time < as.Date("2023-05-22"))
plot(tsd_data)

disease_threshold <- estimate_disease_threshold(tsd_data)

multiple_waves <- combined_seasonal_output(
  tsd_data,
  disease_threshold = disease_threshold$disease_threshold,
  multiple_waves = TRUE,
  burden_level_decrease = "low",
  steps_with_decrease = 2
)