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   1 #' Incidence Decay (ID)
   2 #'
   3 #' This function implements a least squares estimation method of R0 due to
   4 #' Fisman et al. (PloS One, 2013). See details for implementation notes.
   5 #'
   6 #' The method is based on a straightforward incidence decay model. The estimate
   7 #' of R0 is the value which minimizes the sum of squares between observed case
   8 #' counts and cases counts expected under the model.
   9 #'
  10 #' This method is based on an approximation of the SIR model, which is most
  11 #' valid at the beginning of an epidemic. The method assumes that the mean of
  12 #' the serial distribution (sometimes called the serial interval) is known. The
  13 #' final estimate can be quite sensitive to this value, so sensitivity testing
  14 #' is strongly recommended. Users should be careful about units of time (e.g.,
  15 #' are counts observed daily or weekly?) when implementing.
  16 #'
  17 #' @param cases Vector of case counts. The vector must be non-empty and only
  18 #'   contain positive integers.
  19 #' @param mu Mean of the serial distribution. This must be a positive number.
  20 #'   The value should match the case counts in time units. For example, if case
  21 #'   counts are weekly and the serial distribution has a mean of seven days,
  22 #'   then `mu` should be set to `1`. If case counts are daily and the serial
  23 #'   distribution has a mean of seven days, then `mu` should be set to `7`.
  24 #'
  25 #' @return An estimate of the basic reproduction number (R0).
  26 #'
  27 #' @references [Fisman et al. (PloS One, 2013)](
  28 #' https://doi.org/10.1371/journal.pone.0083622)
  29 #'
  30 #' @seealso [idea()] for a similar method.
  31 #'
  32 #' @export
  33 #'
  34 #' @examples
  35 #' # Weekly data.
  36 #' cases <- c(1, 4, 10, 5, 3, 4, 19, 3, 3, 14, 4)
  37 #'
  38 #' # Obtain R0 when the serial distribution has a mean of five days.
  39 #' id(cases, mu = 5 / 7)
  40 #'
  41 #' # Obtain R0 when the serial distribution has a mean of three days.
  42 #' id(cases, mu = 3 / 7)
  43 id <- function(cases, mu) {
  44   exp(sum((log(cases) * mu) / seq_along(cases)) / length(cases))
  45 }