  Contact matrices have become a key ingredient of modern epidemic models. They
account for the stratification of contacts for the age of individuals and, in
some cases, the context of their interactions. However, age and context are not
the only factors shaping contact structures and affecting the spreading of
infectious diseases. Socio-economic status (SES) variables such as wealth,
ethnicity, and education play a major role as well. Here, we introduce
generalized contact matrices capable of stratifying contacts across any number
of dimensions including any SES variable. We derive an analytical expression
for the basic reproductive number of an infectious disease unfolding on a
population characterized by such generalized contact matrices. Our results, on
both synthetic and real data, show that disregarding higher levels of
stratification might lead to the under-estimation of the reproductive number
and to a mis-estimation of the global epidemic dynamics. Furthermore, including
generalized contact matrices allows for more expressive epidemic models able to
capture heterogeneities in behaviours such as different levels of adoption of
non-pharmaceutical interventions across different groups. Overall, our work
contributes to the literature attempting to bring socio-economic, as well as
other dimensions, to the forefront of epidemic modeling. Tackling this issue is
crucial for developing more precise descriptions of epidemics, and thus to
design better strategies to contain them.
