Polynomial epidemics and clustering in contact networks

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.