#' MLE for complete general stochastic epidemic model
#'
#' Compute MLE for complete epidemic observations.
#'
#' @param r numeric vector: removal times
#' @param i numeric vector: infection times
#' @param N integer: population size
#'
#' @return MLE for (beta, gamma)
#'
#' @export
mle_complete_gsem = function(r, i, N){
n = length(r)
t = 0
for(j in 1:n){
t = t + sum(sapply(i, min, r[j]) - sapply(i, min, i[j]))
}
ri = sum(r - i)
g = n / ri
b = (n - 1) / (t + (N - n) * ri) * N
return(c(b,g))
}
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