  The spread of an infectious disease can be promoted by previous infections
with other pathogens. This cooperative effect can give rise to violent
outbreaks, reflecting the presence of an abrupt epidemic transition. As for
other diffusive dynamics, the topology of the interaction pattern of the host
population plays a crucial role. It was conjectured that a discontinuous
transition arises when there are relatively few short loops and many long loops
in the contact network. Here we focus on the role of local clustering in
determining the nature of the transition. We consider two mutually cooperative
pathogens diffusing in the same population: an individual already infected with
one disease has an increased probability of getting infected by the other. We
look at how a disease obeying the susceptible-infected-removed dynamics spreads
on contact networks with tunable clustering. Using numerical simulations we
show that for large cooperativity the epidemic transition is always abrupt,
with the discontinuity decreasing as clustering is increased. For large
clustering strong finite size effects are present and the discontinuous nature
of the transition is manifest only in large networks. We also investigate the
problem of influential spreaders for cooperative infections, revealing that
both cooperativity and clustering strongly enhance the dependence of the
spreading influence on the degree of the initial seed.
