  This work presents a model combining the simplest communicable and
non-communicable disease models. The latter is, by far, the leading cause of
sickness and death in the World, and introduces basal heterogeneity in
populations where communicable diseases evolve. The model can be interpreted as
a risk-structured model, another way of accounting for population
heterogeneity.
  Our results show that considering the non-communicable disease (in the end,
heterogeneous populations) allows the communicable disease to become endemic
even if the basic reproduction number is less than $1$. This feature is known
as subcritical bifurcation. Furthermore, ignoring the non-communicable disease
dynamics results in overestimating the reproduction number and, thus, giving
wrong information about the actual number of infected individuals. We calculate
sensitivity indices and derive interesting epidemic-control information.
