Exponential extinction time of the contact process on rank-one   inhomogeneous random graphs
  We show that the contact process on the rank-one inhomogeneous random graphs and Erdos-R{\'e}nyi 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. 
Van Hao Can (I2M)
math.PR math.CO