  We study implications of the dynamical and spatial contact structure between
Brazilian escorts and sex-buyers for the spreading of sexually transmitted
infections (STI). Despite a highly skewed degree distribution diseases
spreading in this contact structure have rather well-defined epidemic
thresholds. Temporal effects create a broad distribution of outbreak sizes even
if the transmission probability is taken to the hypothetical value of 100%.
Temporal correlations speed up outbreaks, especially in the early phase,
compared to randomized contact structures. The time-ordering and the network
topology, on the other hand, slow down the epidemics. Studying compartmental
models we show that the contact structure can probably not support the spread
of HIV, not even if individuals were sexually active during the acute
infection. We investigate hypothetical means of containing an outbreak and find
that travel restrictions are about as efficient as removal of the vertices of
highest degree. In general, the type of commercial sex we study seems not like
a major factor in STI epidemics.
