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Copy file name to clipboardExpand all lines: contact-matrices.md
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@@ -36,6 +36,7 @@ Some groups of individuals have more contacts than others; the average schoolchi
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```r
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library(contactsurveys)
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library(socialmixr)
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```
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@@ -78,25 +79,53 @@ For a contact matrix with rows $i$ and columns $j$:
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Contact matrices are commonly estimated from studies that use diaries to record interactions. For example, the POLYMOD survey measured contact patterns in 8 European countries using data on the location and duration of contacts reported by the study participants [(Mossong et al. 2008)](https://doi.org/10.1371/journal.pmed.0050074).
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The R package `{socialmixr}` contains functions which can estimate contact matrices from POLYMOD and other surveys. We can load the POLYMOD survey data:
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The R package `{socialmixr}` contains functions which can estimate contact matrices from POLYMOD and other surveys. We can download and load the POLYMOD survey data directly from Zenodo using `{contactsurveys}` and `{socialmixr}`:
Always pass the `countries =` argument to `contact_matrix()` to make sure you use data from the intended country only.
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::::::::::::::::::::::::::::::::::::::::::::::::
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Then we can obtain the contact matrix for the age categories we want by specifying `age_limits`. We also add `return_demography = TRUE` to include demographic information in the output, which is required when using the contact matrix with `{epidemics}`.
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```r
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contact_data<-socialmixr::contact_matrix(
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survey=polymod,
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contacts_byage<-socialmixr::contact_matrix(
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survey=survey_load,
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countries="United Kingdom",
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age_limits= c(0, 20, 40),
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symmetric=TRUE
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symmetric=TRUE,
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return_demography=TRUE
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)
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contact_data
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contacts_byage
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```
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```output
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**Note: although the contact matrix `contact_data$matrix` is not itself mathematically symmetric, it satisfies the condition that the total number of contacts of one group with another is the same as the reverse. In other words:
**Note: although the contact matrix `contacts_byage$matrix` is not itself mathematically symmetric, it satisfies the condition that the total number of contacts of one group with another is the same as the reverse. In other words:
For the mathematical explanation see [the corresponding section in the socialmixr documentation](https://epiforecasts.io/socialmixr/articles/socialmixr.html#symmetric-contact-matrices).**
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::::::::::::::::::::::::::::::::::::::::::::::::
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The example above uses the POLYMOD survey. There are a number of surveys available in `socialmixr`. To list the available surveys, use `socialmixr::list_surveys()`. To download a survey, we can use `socialmixr::get_survey()`
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The example above uses the POLYMOD survey. There are a number of surveys available in `socialmixr`. To list the available surveys, use `socialmixr::list_surveys()`. To download a survey from Zenodo and load it, we use `contactsurveys::download_survey()` followed by `socialmixr::load_survey()`:
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```r
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# Access the contact survey data from Zenodo
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zambia_sa_survey<-socialmixr::get_survey(
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"https://doi.org/10.5281/zenodo.3874675"
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# Download and load the contact survey data for Zambia from Zenodo
# Print the vector of population size for {epidemics}
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contact_data_zambia$demography$population
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contacts_byage_zambia$demography$population
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```
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```output
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Rather than just using the raw number of contacts, we can instead normalise the contact matrix to make it easier to work in terms of $R_0$. In particular, we normalise the matrix by scaling it so that if we were to calculate the average number of secondary cases based on this normalised matrix, the result would be 1 (in mathematical terms, we are scaling the matrix so the largest eigenvalue is 1). This transformation scales the entries but preserves their relative values.
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In the case of the above model, we want to define $\beta C_{i,j}$ so that the model has a specified valued of $R_0$. If the entry of the contact matrix $C[i,j]$ represents the contacts of population $i$ with $j$, it is equivalent to `contact_data$matrix[i,j]`, and the maximum eigenvalue of this matrix represents the typical magnitude of contacts, not typical magnitude of transmission. We must therefore normalise the matrix $C$ so the maximum eigenvalue is one; we call this matrix $C_{normalised}$. Because the rate of recovery is $\gamma$, individuals will be infectious on average for $1/\gamma$ days. So $\beta$ as a model input is calculated from $R_0$, the scaling factor and the value of $\gamma$ (i.e. mathematically we use the fact that the dominant eigenvalue of the matrix $R_0 \times C_{normalised}$ is equal to $\beta / \gamma$).
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In the case of the above model, we want to define $\beta C_{i,j}$ so that the model has a specified valued of $R_0$. If the entry of the contact matrix $C[i,j]$ represents the contacts of population $i$ with $j$, it is equivalent to `contacts_byage$matrix[i,j]`, and the maximum eigenvalue of this matrix represents the typical magnitude of contacts, not typical magnitude of transmission. We must therefore normalise the matrix $C$ so the maximum eigenvalue is one; we call this matrix $C_{normalised}$. Because the rate of recovery is $\gamma$, individuals will be infectious on average for $1/\gamma$ days. So $\beta$ as a model input is calculated from $R_0$, the scaling factor and the value of $\gamma$ (i.e. mathematically we use the fact that the dominant eigenvalue of the matrix $R_0 \times C_{normalised}$ is equal to $\beta / \gamma$).
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