Getting started with modelling interventions targeting social contacts

library(epidemics)
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(ggplot2)

Prepare population and initial conditions

Prepare population and contact data.

Note on social contacts data

epidemics expects social contacts matrices $M_{ij}$ to represent contacts to $i$ from $j$(Wallinga, Teunis, and Kretzschmar 2006), such that $q M_{ij} / n_i$ is the probability of infection, where $q$ is a scaling factor dependent on infection transmissibility, and $n_i$ is the population proportion of group $i$.

Social contacts matrices provided by the socialmixr package follow the opposite convention, where $M_{ij}$ represents contacts from group $i$ to group $j$.

Thus social contact matrices from socialmixr need to be transposed (using t()) before they are used with epidemics.

# 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),
  symmetric = TRUE
)
#> Removing participants that have contacts without age information. To change this behaviour, set the 'missing.contact.age' option

# prepare contact matrix
contact_matrix <- t(contact_data$matrix)

# prepare the demography vector
demography_vector <- contact_data$demography$population
names(demography_vector) <- rownames(contact_matrix)

Prepare initial conditions for each age group.

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

# build for all age groups
initial_conditions <- rbind(
  initial_conditions,
  initial_conditions,
  initial_conditions
)

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

Prepare a population as a population class object.

uk_population <- population(
  name = "UK",
  contact_matrix = contact_matrix,
  demography_vector = demography_vector,
  initial_conditions = initial_conditions
)

Prepare an intervention

Prepare an intervention to simulate school closures.

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

# examine the intervention object
close_schools
#> <contacts_intervention> object
#> 
#>  Intervention name: 
#> "School closure"
#> 
#>  Begins at: 
#> [1] 200
#> 
#>  Ends at: 
#> [1] 300
#> 
#>  Reduction: 
#>              Interv. 1
#> Demo. grp. 1     0.500
#> Demo. grp. 2     0.001
#> Demo. grp. 3     0.001

Run epidemic model

# run an epidemic model using `epidemic`
output <- model_default(
  population = uk_population,
  intervention = list(contacts = close_schools),
  time_end = 600, increment = 1.0
)

Prepare data and visualise infections

Plot epidemic over time, showing only the number of individuals in the exposed and infected compartments.

# plot figure of epidemic curve
filter(output, compartment %in% c("exposed", "infectious")) %>%
  ggplot(
    aes(
      x = time,
      y = value,
      col = demography_group,
      linetype = compartment
    )
  ) +
  geom_line() +
  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"
  ) +
  scale_y_continuous(
    labels = scales::comma
  ) +
  scale_colour_brewer(
    palette = "Dark2",
    name = "Age group"
  ) +
  expand_limits(
    y = c(0, 500e3)
  ) +
  coord_cartesian(
    expand = FALSE
  ) +
  theme_bw() +
  theme(
    legend.position = "top"
  ) +
  labs(
    x = "Simulation time (days)",
    linetype = "Compartment",
    y = "Individuals"
  )

References

Wallinga, Jacco, Peter Teunis, and Mirjam Kretzschmar. 2006. “Using Data on Social Contacts to Estimate Age-Specific Transmission Parameters for Respiratory-Spread Infectious Agents.” American Journal of Epidemiology 164 (10): 936–44. https://doi.org/10.1093/aje/kwj317.