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We consider the contact process on a random graph with fixed degreedistribution given by a power law. We follow the work of Chatterjee andDurrett, who showed that for arbitrarily small infection parameter $\lambda$,the survival time of the process is larger than a stretched exponentialfunction of the number of vertices, $n$. We obtain sharp bounds for the typicaldensity of infected sites in the graph, as $\lambda$ is kept fixed and $n$tends to infinity. We exhibit three different regimes for this density,depending on the tail of the degree law.

Metastable Densities for Contact Processes on Power Law Random Graphs