Simulate Pandemic Scenarios with Uncertainty

What do we have?

• Daily aggregate of incident Flu cases
• Serial interval distribution
• Infectious period

Steps in code

# Pandemic scenarios with uncertainty -----------------------------------------

# Load packages
library(epidemics)
library(EpiEstim) # for Rt estimation
library(tidyverse)
library(withr)

# Generate an R estimate with EpiEstim ----------------------------------------

# get 2009 influenza data from school in Pennsylvania
data(Flu2009)
flu_early_data <- dplyr::filter(Flu2009$incidence, dates < "2009-05-10")

# define a PDF for the distribution of serial intervals
serial_pdf <- dgamma(seq(0, 25), shape = 2.622, scale = 0.957)

# ensure probabilities add up to 1 by normalising them by the sum
serial_pdf <- serial_pdf / sum(serial_pdf)

# Use EpiEstim to estimate R with uncertainty
# Uses Gamma distribution by default
output_R <- EpiEstim::estimate_R(
  incid = flu_early_data,
  method = "non_parametric_si",
  config = make_config(list(si_distr = serial_pdf))
)

# Plot output to visualise
# plot(output_R, "R")

# get mean mean and sd over time
r_estimate_mean <- mean(output_R$R$`Mean(R)`)
r_estimate_sd <- mean(output_R$R$`Std(R)`)

# Generate 100 R samples
r_samples <- withr::with_seed(
  seed = 1,
  code = rnorm(
    n = 100, 
    mean = r_estimate_mean, 
    sd = r_estimate_sd
  )
)

# Set up the transmission model -------------------------------------------

# load contact and population data from socialmixr::polymod
polymod <- socialmixr::polymod
contact_data <- socialmixr::contact_matrix(
  polymod,
  countries = "United Kingdom",
  age.limits = c(0, 20, 40), # use three age groups
  symmetric = TRUE
)

# prepare contact matrix and demography vector for use in model
# transpose so R0 calculated correctly inside model
contact_matrix <- t(contact_data$matrix) 
demography_vector <- contact_data$demography$population
names(demography_vector) <- rownames(contact_matrix)

# initial conditions
initial_i <- 1e-6
initial_conditions <- c(
  S = 1 - initial_i, E = 0, I = initial_i, R = 0, V = 0
)

# define same ICs for all age groups
initial_conditions <- rbind(
  initial_conditions,
  initial_conditions,
  initial_conditions
)

# assign rownames for clarity
rownames(initial_conditions) <- rownames(contact_matrix)

# define UK population object
uk_population <- epidemics::population(
  name = "UK",
  contact_matrix = contact_matrix,
  demography_vector = demography_vector,
  initial_conditions = initial_conditions
)

# Simulate scenario with uncertainty --------------------------------------

# define epidemic parameters
infectious_period <- 7
beta <- r_samples / infectious_period

# pass the vector of transmissibilities to the basic {epidemics} model
output <- epidemics::model_default(
  population = uk_population,
  transmission_rate = beta,
  recovery_rate = 1 / infectious_period,
  time_end = 600
)

# select the parameter set and data columns with dplyr::select()
# add the R value for visualisation
# calculate new infections, and use tidyr to unnest the data column
data <- dplyr::select(output, param_set, transmission_rate, data) %>%
  mutate(
    r_value = r_samples,
    new_infections = purrr::map(data, new_infections)
  ) %>%
  dplyr::select(-data) %>%
  tidyr::unnest(new_infections)


# Plot outputs ------------------------------------------------------------

# # plot the data
# data %>% 
#   dplyr::filter() %>%
#   ggplot() +
#   geom_line(
#     aes(time, new_infections, col = r_value, group = param_set),
#     alpha = 0.3
#   ) +
#   # use qualitative scale to emphasize differences
#   scale_colour_fermenter(
#     palette = "Dark2",
#     name = "R",
#     breaks = c(0, 1, 1.5, 2.0, 3.0),
#     limits = c(0, 3)
#   ) +
#   scale_y_continuous(
#     name = "New infections",
#     labels = scales::label_comma(scale = 1e-3, suffix = "K")
#   ) +
#   labs(
#     x = "Time (days since start of epidemic)"
#   ) +
#   facet_grid(
#     cols = vars(demography_group)
#   ) +
#   theme_bw() +
#   theme(
#     legend.position = "top",
#     legend.key.height = unit(2, "mm")
#   )

# Add an intervention -----------------------------------------------------

# prepare a school-closure intervention with a differential effect on age groups
close_schools <- epidemics::intervention(
  name = "School closure",
  type = "contacts",
  time_begin = 200,
  time_end = 300,
  reduction = matrix(c(0.5, 0.001, 0.001))
)

# run model with intervention
output <- epidemics::model_default(
  population = uk_population,
  transmission_rate = beta,
  recovery_rate = 1 / infectious_period,
  intervention = list(contacts = close_schools),
  time_end = 600
)

# reformat data for plotting
data <- dplyr::select(output, param_set, transmission_rate, data) %>%
  dplyr::mutate(
    r_value = r_samples,
    new_infections = map(data, new_infections)
  ) %>%
  dplyr::select(-data) %>%
  tidyr::unnest(new_infections)


# plot the data
data %>% 
  dplyr::filter() %>%
  ggplot() +
  geom_line(
    aes(time, new_infections, col = r_value, group = param_set),
    alpha = 0.3
  ) +
  # use qualitative scale to emphasize differences
  scale_colour_fermenter(
    palette = "Dark2",
    name = "R",
    breaks = c(0, 1, 1.5, 2.0, 3.0),
    limits = c(0, 3)
  ) +
  scale_y_continuous(
    name = "New infections",
    labels = scales::label_comma(scale = 1e-3, suffix = "K")
  ) +
  labs(
    x = "Time (days since start of epidemic)"
  ) +
  facet_grid(
    cols = vars(demography_group)
  ) +
  theme_bw() +
  theme(
    legend.position = "top",
    legend.key.height = unit(2, "mm")
  ) +
  annotate(
    geom = "rect",
    xmin = close_schools$time_begin,
    xmax = close_schools$time_end,
    ymin = 0, ymax = 500e3,
    fill = alpha("red", alpha = 0.2),
    lty = "dashed"
  ) +
  annotate(
    geom = "text",
    x = mean(c(close_schools$time_begin, close_schools$time_end)),
    y = 400e3,
    angle = 90,
    label = "School closure"
  ) +
  expand_limits(
    y = c(0, 500e3)
  ) +
  coord_cartesian(
    expand = FALSE
  ) 

Steps in detail

• {EpiEstim} estimates Rt.
• {socialmixr} get access to social contact data.
• {epidemics} create epidemic scenario models.
• {tidyverse} imports the pipe %>%, {dplyr} and {ggplot2}.

Please note that the code assumes the necessary packages are already installed. If they are not, you can install them using first the install.packages("pak") function and then the pak::pak() function for both packages in CRAN or GitHub before loading them with library().

Related

• Explanation on Modelling parameter uncertainty
• Explanation on Modelling overlapping and sequential interventions targeting social contacts