Polynomial epidemics and clustering in contact networks

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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.