Symmetrise a contact matrix

Makes a contact matrix symmetric so that \(c_{ab} N_a = c_{ba} N_b\), where \(c_{ab}\) is the (a, b) entry and \(N_a\) is the population of group a. Each pair is replaced by half their sum, weighted by population size. Reciprocity requires that each grouping has the same levels on the participant and contact side; if not, the function aborts.

Usage

symmetrise(x, survey_pop, symmetric_norm_threshold = 2)

Arguments

x

a list as returned by compute_matrix(), with elements matrix and participants

survey_pop

a data frame; see Population data below

symmetric_norm_threshold

threshold for the normalisation factor before issuing a warning (default 2)

Value

x with $matrix replaced by the symmetrised version

Population data

survey_pop is a data frame with one column per grouping, named after the grouping (e.g. age, gender) and holding that grouping's levels as they appear in the matrix, plus a population column with the size of each combination. One row per combination of levels is required, and levels are matched to the matrix exactly, without interpolation.

Use align_ages() to build this from a raw population table: it aggregates each grouping to the matrix's levels (interpolating the age grouping where needed) and labels the columns to match.

Examples

data(polymod)
result <- polymod |>
  (\(s) s[country == "United Kingdom"])() |>
  assign_age_groups(age_limits = c(0, 5, 15)) |>
  compute_matrix()
uk_pop <- data.frame(
  age = limits_to_agegroups(0:80, notation = "brackets"),
  population = rep(1e5, 81)
)
result |> symmetrise(survey_pop = align_ages(uk_pop, result))
#> 
#> ── Contact matrix (3 age groups) ──
#> 
#> Ages: "[0,5)", "[5,15)", and "[15,Inf)"
#> Participants: 1011
#> 
#>           contact.age.group
#> age.group      [0,5)   [5,15) [15,Inf)
#>   [0,5)    1.9157895 1.245201 5.340124
#>   [5,15)   0.6226006 7.946078 7.367253
#>   [15,Inf) 0.4045549 1.116250 9.594101