Anomalous behavior of the contact process with aging

The effect of power-law aging on a contact process is studied by simulation and using a mean-held approach. The introduced type of aging accounts for, e.g., the growth of the virus fitness (HIV infection). We find that the system may approach its stationary state in a nontrivial, nonmonotonous way. For the particular value of the aging exponent alpha =1 we observe a rich set of behaviors: depending on the process parameters, the relaxation to the stationary state proceeds as 1/ln t or via a power law with a nonuniversal exponent. Simulation results suggest that for 0<<alpha><1, the absorbing-state phase transition is in the universality class of directed percolation.