Exposure in finalsize population

exposure_probability.R

# Define R0
r_number <- 1.4

# Final size model
attack_rate <- finalsize::final_size(r_number)$n_infected

print(attack_rate)

# Calculate total exposures over the whole epidemic
# (note: later in epidemic, now-immune people will be re-exposed)
expected_exposures <- attack_rate*r_number

# Calculate the expected proportion of the population with at least exposure
expected_proportion_exact <- function(X, # total exposures
                                      N # total population size
                                      ) {
  return(1 - (1 - 1/N)^X)
}

# Can for large N, can approximate with:
expected_proportion <- function(Y) {
  return(1 - exp(-Y))
}
# where Y = X/N

# Calculate proportion exposed at least once:
result_exact <- expected_proportion(expected_exposures)

# Probability exposed k times follows a binomial, but because X and N large, can use 
# Poisson approximation with lambda = X/N
exposed_k_times <- 0:5
probability_exposed <- dpois(exposed_k_times, lambda = expected_exposures)

# Plot results
plot(exposed_k_times, probability_exposed)