## Contact matrices

European Union contact matrices

Contact matrices by 1-year age brackets are available for 26 European countries, namely Austria, Bulgaria, Switzerland, Czech Republic, Germany, Denmark, Spain, Estonia, Finland, France, United Kingdom, Greece, Hungary, Ireland, Italy, Lithuania, Luxembourg, Latvia, The Netherlands, Norway, Portugal, Romania, Slovakia, Slovenia, Sweden, Cyprus.

File M.xls contains country-specific total matrices of adequate contacts by age, obtained by aggregating contacts in households, schools, workplaces and general community, as presented in Fumanelli et al., PLoS Computational Biology, 2012. These matrices can be directly employed in transmission models: since they represent frequencies of contacts by age, the average number of contacts by age can be obtained by multiplying the matrices by a certain, unknown scale factor that we assume to be embedded in the transmission rate. Therefore, when multiplied by the vectors representing the fractions of infectives by age, they provide the average number of infective contacts by age, as required by the classic theory of age-structured SEIR models.

For instance, the equation for susceptibles of age i would read

where α is the transmission probability and q is the scale factor.

File HSWR.xls contains setting-specific matrices of adequate contacts (household, school, workplace, general community) for the 26 countries.

Since one may be interested in considering different age classes, we also provide the symmetric versions which represent the total number of contacts by age (files M-symm.xls and HSWR-symm.xls). To obtain the total number of contacts for the desired age brackets, it is sufficient to sum the corresponding entries of the symmetric matrices.

Please note that disease transmission models usually require the average number of contacts by age; these can be obtained by dividing the user-defined symmetric matrices by the corresponding age structure of the population.

Therefore, for instance, matrices in M.xls (or HSWR.xls) can be obtained from the corresponding matrices in M-symm.xls (or HSWR-symm.xls) by dividing each element (say, mij) by Ni, where Ni is the number of individuals of age i in the population.

Age structures by 1-year brackets can be retrieved at the Eurostat website:
http://epp.eurostat.ec.europa.eu/portal/page/portal/eurostat/home/

Please note that matrices provided as Supporting Information in Fumanelli et al., PLoS Comput Biol 2012 are slightly different from those in files HSWR-symm.xls and M-symm.xls. The difference consists just in a multiplying factor, which does not affect their usage in epidemic modeling.

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