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Contact Matrix Examples

contact_matrix_examples.Rmd

This vignette demonstrates how to set up contact matrices for age- and school-structured models using examples.

First we define the age groups we want to use, and the population sizes of each group:

# under 1, 1-4, 5-11, 12-13, 14-17, 18-24, 25-44, 45-69, 70 plus
agelims <- c(0, 1, 5, 12, 14, 18, 25, 45, 70)
agepops <- c(100, 400, 700, 200, 400, 700, 2000, 2400, 1000)

Here’s how to generate a contact matrix using Polymod data, which is contact survey data from the well known “Polymod” study. When including the second argument to the contactMatrixPolymod() function, the contact matrix will be adjusted to fit the population distribution defined above in the agepops variable.

cmp <- contactMatrixPolymod(agelims, agepops)
knitr::kable(round(cmp, 2), format = "markdown")
under1 1to4 5to11 12to13 14to17 18to24 25to44 45to69 70+
under1 0.42 0.72 0.57 0.09 0.21 0.32 2.11 1.14 0.13
1to4 0.18 2.98 1.52 0.16 0.24 0.49 3.28 1.89 0.35
5to11 0.08 0.87 8.79 0.82 0.46 0.46 3.35 1.88 0.37
12to13 0.04 0.32 2.86 7.98 2.50 0.57 2.77 2.22 0.47
14to17 0.05 0.24 0.80 1.25 9.67 2.21 2.71 2.51 0.37
18to24 0.05 0.28 0.46 0.16 1.26 5.72 3.68 2.87 0.37
25to44 0.11 0.66 1.17 0.28 0.54 1.29 5.72 3.83 0.61
45to69 0.05 0.32 0.55 0.18 0.42 0.84 3.20 4.27 0.96
70+ 0.01 0.14 0.26 0.09 0.15 0.26 1.22 2.30 1.57

The sum of each row represents the relative overall contact rate of each group:

knitr::kable(round(rowSums(cmp), 2), format = "markdown", col.names = "total")
total
under1 5.72
1to4 11.11
5to11 17.09
12to13 19.74
14to17 19.82
18to24 14.86
25to44 14.20
45to69 10.78
70+ 6.01

Those row sums can be factored out to generate the fraction of each group’s contacts that are with each group: The sum of each row represents the relative overall contact rate of each group:

knitr::kable(round(cmp/rowSums(cmp), 2), format = "markdown")
under1 1to4 5to11 12to13 14to17 18to24 25to44 45to69 70+
under1 0.07 0.13 0.10 0.02 0.04 0.06 0.37 0.20 0.02
1to4 0.02 0.27 0.14 0.01 0.02 0.04 0.29 0.17 0.03
5to11 0.00 0.05 0.51 0.05 0.03 0.03 0.20 0.11 0.02
12to13 0.00 0.02 0.14 0.40 0.13 0.03 0.14 0.11 0.02
14to17 0.00 0.01 0.04 0.06 0.49 0.11 0.14 0.13 0.02
18to24 0.00 0.02 0.03 0.01 0.08 0.38 0.25 0.19 0.03
25to44 0.01 0.05 0.08 0.02 0.04 0.09 0.40 0.27 0.04
45to69 0.00 0.03 0.05 0.02 0.04 0.08 0.30 0.40 0.09
70+ 0.00 0.02 0.04 0.02 0.02 0.04 0.20 0.38 0.26

Now we show how to split the age groups for elementary school (5-11), middle school (12-13), and high school (18-24) into two schools each:

schoolagegroups <- c(3, 3, 4, 4, 5, 5)         #The indices of the age group for each school
schoolpops <- c(350, 350, 100, 100, 200, 200)  #The number of students in each school

The socialmixr R package includes functions that allow us to see the number of contacts of school-aged children that occurred overall vs. just at school:

cmAll <- suppressMessages(
    suppressWarnings(socialmixr::contact_matrix(socialmixr::polymod,
                                                age.limits = agelims)$matrix))
cmSchool <- suppressMessages(
    suppressWarnings(socialmixr::contact_matrix(socialmixr::polymod,
                                                age.limits = agelims,
                                                filter = list(cnt_school = 1))$matrix))

knitr::kable(round(cmAll, 2), format = "markdown")
[0,1) [1,5) [5,12) [12,14) [14,18) [18,25) [25,45) [45,70) 70+
[0,1) 0.33 0.83 0.75 0.10 0.33 0.55 3.72 1.82 0.16
[1,5) 0.07 2.34 1.38 0.19 0.25 0.51 3.62 1.81 0.32
[5,12) 0.03 0.64 7.43 0.86 0.45 0.44 3.68 1.76 0.30
[12,14) 0.03 0.17 1.99 7.14 2.47 0.63 3.35 2.03 0.35
[14,18) 0.01 0.17 0.65 1.07 9.10 2.11 2.98 2.15 0.21
[18,25) 0.01 0.21 0.41 0.13 1.22 5.64 4.14 2.63 0.29
[25,45) 0.04 0.53 1.03 0.23 0.53 1.29 6.55 3.52 0.44
[45,70) 0.02 0.26 0.50 0.18 0.46 0.91 4.01 4.34 0.74
70+ 0.01 0.11 0.25 0.10 0.20 0.31 1.72 2.75 1.48 
knitr::kable(round(cmSchool, 2), format = "markdown")
[0,1) [1,5) [5,12) [12,14) [14,18) [18,25) [25,45) [45,70) 70+
[0,1) 0.14 0.09 0.03 0.00 0.14 0.02 0.31 0.01 0.00
[1,5) 0.01 1.45 0.43 0.02 0.02 0.02 0.47 0.18 0.01
[5,12) 0.00 0.18 5.17 0.40 0.05 0.07 0.72 0.40 0.00
[12,14) 0.00 0.01 0.62 5.57 1.38 0.07 0.86 0.48 0.01
[14,18) 0.01 0.03 0.07 0.46 6.21 0.64 0.76 0.52 0.00
[18,25) 0.00 0.03 0.04 0.01 0.42 2.02 0.36 0.20 0.00
[25,45) 0.00 0.05 0.18 0.02 0.07 0.10 0.27 0.09 0.00
[45,70) 0.00 0.06 0.15 0.04 0.12 0.05 0.11 0.10 0.01
70+ 0.00 0.00 0.01 0.00 0.01 0.00 0.00 0.01 0.00

Based on comparing the diagonal elements for the school-aged children age groups, we have some basis for an assumption that 70% of a student’s within-age-group contacts occur at their own school:

schportion <- 0.70

Now we use the above ingredients to create a new matrix using the contactMatrixAgeSchool() function. We show the old age-structured model and the new age-and-school-structured model for comparison:

cmps <- contactMatrixAgeSchool(agelims, agepops, schoolagegroups, schoolpops, schportion)

knitr::kable(round(cmp,2), format = "markdown")
under1 1to4 5to11 12to13 14to17 18to24 25to44 45to69 70+
under1 0.42 0.72 0.57 0.09 0.21 0.32 2.11 1.14 0.13
1to4 0.18 2.98 1.52 0.16 0.24 0.49 3.28 1.89 0.35
5to11 0.08 0.87 8.79 0.82 0.46 0.46 3.35 1.88 0.37
12to13 0.04 0.32 2.86 7.98 2.50 0.57 2.77 2.22 0.47
14to17 0.05 0.24 0.80 1.25 9.67 2.21 2.71 2.51 0.37
18to24 0.05 0.28 0.46 0.16 1.26 5.72 3.68 2.87 0.37
25to44 0.11 0.66 1.17 0.28 0.54 1.29 5.72 3.83 0.61
45to69 0.05 0.32 0.55 0.18 0.42 0.84 3.20 4.27 0.96
70+ 0.01 0.14 0.26 0.09 0.15 0.26 1.22 2.30 1.57 
knitr::kable(round(cmps,2), format = "markdown")
under1 1to4 5to11s1 5to11s2 12to13s3 12to13s4 14to17s5 14to17s6 18to24 25to44 45to69 70+
under1 0.42 0.72 0.28 0.28 0.04 0.04 0.11 0.11 0.32 2.11 1.14 0.13
1to4 0.18 2.98 0.76 0.76 0.08 0.08 0.12 0.12 0.49 3.28 1.89 0.35
5to11s1 0.08 0.87 7.47 1.32 0.41 0.41 0.23 0.23 0.46 3.35 1.88 0.37
5to11s2 0.08 0.87 1.32 7.47 0.41 0.41 0.23 0.23 0.46 3.35 1.88 0.37
12to13s3 0.04 0.32 1.43 1.43 6.79 1.20 1.25 1.25 0.57 2.77 2.22 0.47
12to13s4 0.04 0.32 1.43 1.43 1.20 6.79 1.25 1.25 0.57 2.77 2.22 0.47
14to17s5 0.05 0.24 0.40 0.40 0.63 0.63 8.22 1.45 2.21 2.71 2.51 0.37
14to17s6 0.05 0.24 0.40 0.40 0.63 0.63 1.45 8.22 2.21 2.71 2.51 0.37
18to24 0.05 0.28 0.23 0.23 0.08 0.08 0.63 0.63 5.72 3.68 2.87 0.37
25to44 0.11 0.66 0.59 0.59 0.14 0.14 0.27 0.27 1.29 5.72 3.83 0.61
45to69 0.05 0.32 0.27 0.27 0.09 0.09 0.21 0.21 0.84 3.20 4.27 0.96
70+ 0.01 0.14 0.13 0.13 0.05 0.05 0.07 0.07 0.26 1.22 2.30 1.57