How to simulate the effective reproductive number (R_eff) with heterogeneity in social contact?

Ingredients

• Account for heterogeneous social contact
• Assume homogeneous susceptibility in all age groups

Steps in code

library(finalsize)
library(socialmixr)
library(tidyverse)

# get UK polymod data
polymod <- socialmixr::polymod
contact_data <- socialmixr::contact_matrix(
  polymod,
  countries = "United Kingdom",
  age.limits = c(0, 5, 18, 40, 65),
  symmetric = TRUE
)

# get the contact matrix and demography data
contact_matrix <- t(contact_data$matrix)

# scale the contact matrix so the largest eigenvalue is 1.0
# this is to ensure that the overall epidemic dynamics correctly reflect
# the assumed value of R0
contact_matrix_scaled <- contact_matrix / max(Re(eigen(contact_matrix)$values))

# Define population in each age group
demography_vector <- contact_data$demography$population
demography_groups <- contact_data$demography$age.group

demography_vector

[1]  3453670  9761554 18110368 19288101  9673058

demography_groups

[1] "[0,5)"   "[5,18)"  "[18,40)" "[40,65)" "65+"    

# divide each row of the contact matrix by the corresponding demography
# this reflects the assumption that each individual in group {j} make contacts
# at random with individuals in group {i}
contact_matrix_random <- contact_matrix_scaled / demography_vector

# Define susceptibility of each group
# susceptibility matrix
susceptibility <- tibble(
  age_group = demography_groups,
  susceptible = c(0.8, 0.8, 0.8, 0.8, 0.8)
) %>%
  column_to_rownames(var = "age_group") %>%
  as.matrix()

susceptibility

        susceptible
[0,5)           0.8
[5,18)          0.8
[18,40)         0.8
[40,65)         0.8
65+             0.8

# Assume uniform susceptibility within age groups
# demography-in-susceptibility matrix
p_susceptibility <- tibble(
  age_group = demography_groups,
  susceptible = c(1.0, 1.0, 1.0, 1.0, 1.0)
) %>%
  column_to_rownames(var = "age_group") %>%
  as.matrix()

p_susceptibility

        susceptible
[0,5)             1
[5,18)            1
[18,40)           1
[40,65)           1
65+               1

# R0 of the disease
r0 <- 1.5 # assumed for pandemic influenza

# calculate the effective R0 using `r_eff()`
r_eff(
  r0 = r0,
  contact_matrix = contact_matrix_random,
  demography_vector = demography_vector,
  susceptibility = susceptibility,
  p_susceptibility = p_susceptibility
)

[1] 1.2

Steps in detail

• (pending)

Related

• Explanation on heterogeneity in social contact
• Explanation on effective reproductive number with heterogeneity in social contact