  It is widely known that the spread of the HIV virus was slower than
exponential in several populations, even at the very beginning of the epidemic.
We show that this implies a significant reduction in the effective reproductive
rate of the epidemic, and describe a general mechanism, related to the
clustering properties of the disease transmission network, capable of
explaining this reduction. Our considerations provide a new angle on polynomial
epidemic processes, and may have implications for the choice of strategy
against such epidemics.
