test_that("probability_emergence works for R <= 1 & mutation_rate = 0", {
  expect_identical(
    probability_emergence(
      R_wild = 0.5, R_mutant = 1.5, mutation_rate = 0, num_init_infect = 1
    ),
    0
  )
})

test_that("probability_emergence works for R_mutant > 1", {
  expect_snapshot(
    probability_emergence(
      R_wild = 0.5, R_mutant = 1.5, mutation_rate = 0.1, num_init_infect = 1
    )
  )
})

test_that("probability_emergence works for multi-type ", {
  expect_snapshot(
    probability_emergence(
      R_wild = 0.5,
      R_mutant = c(0.5, 0.5, 1.5),
      mutation_rate = 0.1,
      num_init_infect = 1
    )
  )
})

test_that("probability_emergence is approx 1 for R >> 1", {
  expect_equal(
    probability_emergence(
      R_wild = 10, R_mutant = 10, mutation_rate = 0.1, num_init_infect = 1
    ),
    1,
    tolerance = 0.01
  )
})

test_that("emergence is equal to epidemic for R > 1 & no mutation", {
  emerge <- c()
  epidemic <- c()
  for (R_i in c(2, 5, 10)) {
    for (num_init_infect in c(1, 5, 10)) {
      emerge <- c(
        emerge,
        probability_emergence(
          R_wild = R_i,
          R_mutant = R_i,
          mutation_rate = 0,
          num_init_infect = num_init_infect
        )
      )
      epidemic <- c(
        epidemic,
        probability_epidemic(R = R_i, k = Inf, num_init_infect = num_init_infect)
      )
    }
  }
  expect_equal(emerge, epidemic, tolerance = 0.01)
})