Estimating the risk of getting infected with Covid at an ADE party

gistfile1.txt

library(ggplot2)
library(RColorBrewer)

# Roughly estimates the number of Covid infectious people at an ADE party(N = 900)
# Main uncertainties:
#   (1) Number of people infectious
#   (2) Number of people a single infectious person infects (R_eff)
#
# For (1), we rely on the number of positive tests from last week. This was 1.5%. Generally, this is an underestimate
# of the true number. Similarly, many people are coming to ADE abroad. We use a distribution over different values below.
# For (2), we assume a uniform distribution ranging from 2 to 8. In poorly ventilated spaces, this could be much higher.

# Assumptions:
#     (1) Independence of people
#     (2) Relationship between proportion of positive tests and proportion of infectious people
#
# Regarding (1), this yields a binomial distribution for the number of people X out of N that are infected.
# Independence doesn't hold (party goers no each other but this might not be a huge deal).
# Regarding (2), this depends on which population is being tested. If testing is done at random, then the proportion of
# positive tests should be close to the prevalence of Covid infections. However, most people who do a test probable have
# some kind of reason to do it, hence are not representative of the population. ChatGPT suggests a multiplier of between
# 0.3 and 0.7 times the positivity rate when testing is targeted to get the prevalence. However, not everybody who has Covid
# does a test, so the reported positivity rate likely underestimates the true positivity rate

custom_theme <- theme_minimal() +
  theme(
    legend.position = 'top',
    plot.title = element_text(size = 14, hjust = 0.50)
  )

get_number_infectious <- function(prevalence) {
  N <- 900
  x <- seq(0, 900, 1)
  probs <- dbinom(x, N, prevalence)
  data.frame(x = x, p = probs, prevalence = prevalence)
}

# In unventilated, crowded spaces R_eff can be very high
get_number_infected <- function(prevalence, R_lo = 2, R_hi = 8) {
  N <- 900
  iter <- 10000
  
  number_infectious <- rbinom(iter, n, prevalence)
  R_eff <- runif(iter, R_lo, R_hi)
  data.frame(x = number_infectious * R_eff)
}

positivity_rate <- 0.015 # 1.5% were reported to test positive last week
prevalence <- positivity_rate * 0.50 # mean of 0.3 and 0.7

df_inf <- rbind(
  get_number_infectious(prevalence),
  # To account for underestimation of the positivity rate
  get_number_infectious(prevalence * 3),
  get_number_infectious(prevalence * 5)
)

cols <- brewer.pal(3, 'Set1')
ggplot(df_inf, aes(x = x, y = p, fill = factor(prevalence))) +
  geom_bar(stat = 'identity') + 
  scale_fill_manual(name = 'Covid prevalence', values = cols) +
  xlim(c(0, 100)) +
  ggtitle('Number of people who could be infectious') +
  facet_wrap(~ prevalence) +
  xlab('Number of people') +
  ylab('Density') +
  custom_theme

# Let's assume that 2.225% are infectious. How many might they infect?
# We integrate this uncertainty over the uncertainty in R_eff
set.seed(1)
prevalence <- reported_positive * 0.50 * 3
num_infected <- get_number_infected(prevalence)

ggplot(num_infected, aes(x = x)) +
  geom_histogram() +
  xlab('Number of people getting infected') +
  ggtitle('Number of people getting infected') +
  ylab('Frequency') +
  custom_theme

# Pretty high
mean(num_infected$x)

# Let's be more advanced and integrate uncertainty about the number of infectious people in there
set.seed(1)
iter <- 10000
prevalence <- runif(iter, reported_positive * 0.50, reported_positive * 0.50 * 5)
num_infected2 <- get_number_infected(prevalence)

ggplot(num_infected2, aes(x = x)) +
  geom_histogram() +
  xlab('Number of people getting infected') +
  ggtitle('Number of people getting infected') +
  ylab('Frequency') +
  custom_theme

# Same mean but fatter tails
mean(num_infected2$x)

# Probability that you get infected (assuming equal mixing)
ggplot(num_infected2, aes(x = x / N)) +
  geom_histogram() +
  xlab('Probability that you get infected') +
  ggtitle('Probability that you get infected') +
  ylab('Frequency') +
  custom_theme