Contacts in context: large-scale setting-specific social mixing matrices from the BBC Pandemic project

Petra Klepac; Adam J Kucharski; Andrew JK Conlan; Stephen Kissler; Maria Tang; Hannah Fry; Julia R Gog

We can deduce more from our reported contacts as the contacts are reciprocal (if person A was in contact with B, that means that the person B was also in contact with person A). On a population level that means that the total number of contacts from age group j to i, must be equal to the total number of contacts from age group i to age group j. As the sample of participants might have a different population structure than the wider population, this step depends on the country-specific population structure: we define w i as the total population size of the age group i. In our case, volunteers needed to be in the UK to participate in the study, so we use the 2018 mid-year estimate of the population structure of the UK (available from ONS [1] ). The reciprocal matrix C = (c ij ) gives the population contact matrix, where c ij = 1 2 (m ij + m ji wi wj ) [29] . The population matrix C is of particular importance for infectious disease dynamics because it is related to the next generation matrix [7, 27] . The next generation matrix N captures how the infection spreads when pathogen is first introduced in a population, and its (i, j) entry gives the expected number of new infections in compartment i produced by in infected individual introduced into compartment j. As a result, the dominant eigenvalue of N is equal to the basic reproduction number R 0 or the expected number of secondary infections caused by a single individual introduced to a completely susceptible population. The relationship between the two matrices is