Exponential extinction time of the contact process on rank-one inhomogeneous random graphs

20 pages, accepted for publication in Journal of Theoretical ProbabilityWe show that the contact process on the rank-one inhomogeneous random graphs and Erdos-Rényi graphs with mean degree large enough survives a time exponential in the size of these graphs for any positive infection rate. In addition, a metastable result for the extinction time is also proved