Table 3 reports the parameters of the contact matrix of distributions introduced above.
In order to account for these heterogeneities, we define a new representation based on a contact matrix of distributions.
In order for the present paper to be self-contained, we report here the contact matrix measured in the hospital ward as well as the newly introduced contact matrix of distributions (CMD).
Here we introduce a novel representation based on a contact matrix of distributions, designed to retain the heterogeneous properties of contact durations among pairs of individuals belonging to given role classes.
The matrix is defined so that the entry for role classes X and Y consists of the parameters of the negative binomial distribution that fits the empirical distribution of contact durations between all pairs of individuals x in class X and y in class Y. Similarly to the customary contact matrices, the contact matrix of distributions is not an individual-based representation.
Other perspectives include testing data-driven containment strategies based on the various contact patterns representations and understanding how the evaluation of their performance depends on the representation, in particular for the case of the novel representation defined by the contact matrix of distributions we introduced here.
A particularly interesting validation would be to extract a contact matrix of distributions from one set of data, e.g. in a hospital, to use it to design efficient containment strategies, and then to apply these strategies to a simulated epidemic on another dataset for a similar environment, for instance another hospital.
On the other hand, the contact matrix of distributions (CMD) affords a very good qualitative and quantitative agreement with the spreading patterns obtained with the heterogeneous network representation (HET), even though the CMD representation contains significantly less information on the contact network structure than HET (see Table 1).
In the CMD and CMB cases we also performed 16,000 runs, obtained by generating 1,600 different contact network samples from the fitted contact matrices of distributions, and by simulating for each of them 10 realizations of the epidemic spread.
We have thus built daily contact networks, as well as daily contact matrices and daily contact matrices of distributions: these representations take into account the fact that not all individuals are present every day, and that the contact patterns can vary from one day to the next.
