Disordered one-dimensional contact process

New theoretical and numerical analysis of the one-dimensional contact process with quenched disorder are presented. We derive new scaling relations, different from their counterparts in the pure model, which are valid not only at the critical point but also away from it due to the presence of generic scale invariance. All the proposed scaling laws are verified in numerical simulations. In addition we map the disordered contact process into a Non-Markovian contact process by using the so called Run Time Statistic, and write down the associated field theory. This turns out to be in the same universality class as one derived by Janssen for the quenched system with a Gaussian distribution of impurities. Our findings here support the lack of universality suggested by the field theoretical analysis: generic power-law behaviors are obtained, evidence is shown of the absence of a characteristic time away from the critical point, and the absence of universality is put forward. The intermediate sublinear regime predicted by Bramsom et al. is also found.