diff --git a/R/correlation.R b/R/correlation.R
index df5f88f5..458a3015 100644
--- a/R/correlation.R
+++ b/R/correlation.R
@@ -24,11 +24,11 @@ CorrelationParameters <- R6::R6Class(
   public = list(
 
     #' @description initialise correlation parameters
-    #' @param parameters model parameters
-    initialize = function(parameters) {
-      # Find a list of enabled interventions
-      enabled <- vlapply(INTS, function(name) parameters[[name]])
-      private$interventions <- INTS[enabled]
+    #' @param population popularion size
+    #' @param interventions character vector with the name of enabled interventions
+    initialize = function(population, interventions) {
+      private$population <- population
+      private$interventions <- interventions
 
       # Initialise a rho matrix for our interventions
       n_ints <- private$n_ints()
@@ -38,9 +38,6 @@ CorrelationParameters <- R6::R6Class(
         ncol = n_ints,
         dimnames = list(private$interventions, private$interventions)
       )
-
-      # Store population for mvnorm draws
-      private$population <- parameters$human_population
     },
 
     #' @description Add rho between rounds
@@ -183,7 +180,10 @@ CorrelationParameters <- R6::R6Class(
 #' 
 #' # You can now pass the correlation parameters to the run_simulation function
 get_correlation_parameters <- function(parameters) {
-  CorrelationParameters$new(parameters)
+  # Find a list of enabled interventions
+  enabled <- vlapply(INTS, function(name) parameters[[name]])
+
+  CorrelationParameters$new(parameters$human_population, INTS[enabled])
 }
 
 #' @title Sample a population to intervene in given the correlation parameters
diff --git a/tests/testthat/test-correlation.R b/tests/testthat/test-correlation.R
index 880221ba..882831f8 100644
--- a/tests/testthat/test-correlation.R
+++ b/tests/testthat/test-correlation.R
@@ -1,105 +1,136 @@
 test_that('1 correlation between rounds gives sensible samples', {
   pop <- 1e6
   target <- seq(pop)
-  vaccine_coverage <- .2
-  parameters <- get_parameters(list(
-    human_population = pop,
-    pev = TRUE
-  ))
-  correlations <- get_correlation_parameters(parameters)
+
+  coverage_1 <- .2
+  coverage_2 <- .4
+
+  correlations <- CorrelationParameters$new(pop, c('pev'))
   correlations$inter_round_rho('pev', 1)
-  round_1 <- sample_intervention(target, 'pev', vaccine_coverage, correlations)
-  round_2 <- sample_intervention(target, 'pev', vaccine_coverage, correlations)
-  expect_equal(sum(round_1), pop * .2, tolerance=1e2)
-  expect_equal(sum(round_2), pop * .2, tolerance=1e2)
-  expect_equal(sum(round_1 & round_2), pop * .2, tolerance=1e2)
+
+  round_1 <- sample_intervention(target, 'pev', coverage_1, correlations)
+  round_2 <- sample_intervention(target, 'pev', coverage_2, correlations)
+
+  expect_equal(sum(round_1), pop * coverage_1, tolerance=.1)
+  expect_equal(sum(round_2), pop * coverage_2, tolerance=.1)
+
+  expect_equal(
+    sum(round_1 & round_2),
+    pop * min(coverage_1, coverage_2),
+    tolerance=.1)
+
+  expect_equal(
+    sum(round_1 | round_2),
+    pop * max(coverage_1, coverage_2),
+    tolerance=.1)
 })
 
 test_that('0 correlation between rounds gives sensible samples', {
   pop <- 1e6
   target <- seq(pop)
-  vaccine_coverage <- .5
-  parameters <- get_parameters(list(
-    human_population = pop,
-    pev = TRUE
-  ))
-  correlations <- get_correlation_parameters(parameters)
+
+  coverage_1 <- .2
+  coverage_2 <- .4
+
+  correlations <- CorrelationParameters$new(pop, c('pev'))
   correlations$inter_round_rho('pev', 0)
-  round_1 <- sample_intervention(target, 'pev', vaccine_coverage, correlations)
-  round_2 <- sample_intervention(target, 'pev', vaccine_coverage, correlations)
+
+  round_1 <- sample_intervention(target, 'pev', coverage_1, correlations)
+  round_2 <- sample_intervention(target, 'pev', coverage_2, correlations)
+
+  expect_equal(sum(round_1), pop * coverage_1, tolerance=.1)
+  expect_equal(sum(round_2), pop * coverage_2, tolerance=.1)
+
   expect_equal(
-    length(intersect(which(round_1), which(round_2))),
-    pop * .5,
-    tolerance=1e2
-  )
-  expect_equal(sum(round_1), sum(round_2), tolerance=1e2)
-  expect_equal(sum(round_1), pop * .5, tolerance=1e2)
+    sum(round_1 & round_2),
+    pop * coverage_1 * coverage_2,
+    tolerance=.1)
+
+  expect_equal(
+    sum(round_1 | round_2),
+    pop * (coverage_1 + coverage_2 - (coverage_1 * coverage_2)),
+    tolerance=.1)
 })
 
 test_that('1 correlation between interventions gives sensible samples', {
   pop <- 1e6
   target <- seq(pop)
-  vaccine_coverage <- .2
-  mda_coverage <- .2
-  parameters <- get_parameters(list(
-    human_population = pop,
-    pev = TRUE,
-    mda = TRUE
-  ))
-  correlations <- get_correlation_parameters(parameters)
+
+  pev_coverage <- .2
+  mda_coverage <- .4
+
+  correlations <- CorrelationParameters$new(pop, c('pev', 'mda'))
   correlations$inter_round_rho('pev', 1)
   correlations$inter_round_rho('mda', 1)
   correlations$inter_intervention_rho('pev', 'mda', 1)
-  vaccine_sample <- sample_intervention(target, 'pev', vaccine_coverage, correlations)
+
+  pev_sample <- sample_intervention(target, 'pev', pev_coverage, correlations)
   mda_sample <- sample_intervention(target, 'mda', mda_coverage, correlations)
 
-  expect_equal(sum(vaccine_sample), pop * .2, tolerance=1e2)
-  expect_equal(sum(mda_sample), pop * .2, tolerance=1e2)
-  expect_equal(sum(vaccine_sample & mda_sample), pop * .2, tolerance=1e2)
+  expect_equal(sum(pev_sample), pop * pev_coverage, tolerance=.1)
+  expect_equal(sum(mda_sample), pop * mda_coverage, tolerance=.1)
+
+  expect_equal(
+    sum(pev_sample & mda_sample),
+    pop * min(pev_coverage, mda_coverage),
+    tolerance=.1)
+
+  expect_equal(
+    sum(pev_sample | mda_sample),
+    pop * max(pev_coverage, mda_coverage),
+    tolerance=.1)
 })
 
 test_that('0 correlation between interventions gives sensible samples', {
   pop <- 1e6
   target <- seq(pop)
-  vaccine_coverage <- .2
-  mda_coverage <- .2
-  parameters <- get_parameters(list(
-    human_population = pop,
-    pev = TRUE,
-    mda = TRUE
-  ))
-  correlations <- get_correlation_parameters(parameters)
+
+  pev_coverage <- .2
+  mda_coverage <- .4
+
+  correlations <- CorrelationParameters$new(pop, c('pev', 'mda'))
   correlations$inter_round_rho('pev', 1)
   correlations$inter_round_rho('mda', 1)
   correlations$inter_intervention_rho('pev', 'mda', 0)
-  vaccine_sample <- sample_intervention(target, 'pev', vaccine_coverage, correlations)
+
+  pev_sample <- sample_intervention(target, 'pev', pev_coverage, correlations)
   mda_sample <- sample_intervention(target, 'mda', mda_coverage, correlations)
+
+  expect_equal(sum(pev_sample), pop * pev_coverage, tolerance=.1)
+  expect_equal(sum(mda_sample), pop * mda_coverage, tolerance=.1)
+
   expect_equal(
-    length(intersect(which(vaccine_sample), which(mda_sample))),
-    pop * .5,
-    tolerance=1e2
-  )
-  expect_equal(sum(vaccine_sample), sum(mda_sample), tolerance=1e2)
-  expect_equal(sum(vaccine_sample), pop * .5, tolerance=1e2)
+    sum(pev_sample & mda_sample),
+    pop * pev_coverage * mda_coverage,
+    tolerance=.1)
+
+  expect_equal(
+    sum(pev_sample | mda_sample),
+    pop * (pev_coverage + mda_coverage - (pev_coverage * mda_coverage)),
+    tolerance=.1)
 })
 
 test_that('-1 correlation between interventions gives sensible samples', {
   pop <- 1e6
   target <- seq(pop)
-  vaccine_coverage <- .2
-  mda_coverage <- .2
-  parameters <- get_parameters(list(
-    human_population = pop,
-    pev = TRUE,
-    mda = TRUE
-  ))
-  correlations <- get_correlation_parameters(parameters)
+
+  pev_coverage <- .2
+  mda_coverage <- .4
+
+  correlations <- CorrelationParameters$new(pop, c('pev', 'mda'))
   correlations$inter_round_rho('pev', 1)
   correlations$inter_round_rho('mda', 1)
   correlations$inter_intervention_rho('pev', 'mda', -1)
-  vaccine_sample <- sample_intervention(target, 'pev', vaccine_coverage, correlations)
+
+  pev_sample <- sample_intervention(target, 'pev', pev_coverage, correlations)
   mda_sample <- sample_intervention(target, 'mda', mda_coverage, correlations)
-  expect_equal(length(intersect(which(vaccine_sample), which(mda_sample))), 0)
-  expect_equal(sum(vaccine_sample), .2 * pop, tolerance=1e2)
-  expect_equal(sum(mda_sample), .2 * pop, tolerance=1e2)
+
+  expect_equal(sum(pev_sample), pop * pev_coverage, tolerance=.1)
+  expect_equal(sum(mda_sample), pop * mda_coverage, tolerance=.1)
+
+  expect_equal(sum(pev_sample & mda_sample), 0, tolerance=.1)
+  expect_equal(
+    sum(pev_sample | mda_sample),
+    pop * (pev_coverage + mda_coverage),
+    tolerance=.1)
 })