Critical behavior of the absorbing state transition in the contact process with relaxing immunization

We introduce a model for the Contact Process with relaxing immunization CPRI. In this model, local memory is introduced by a time and space dependence of the contamination probability. The model has two parameters: a typical immunization time τ and a maximum contamination probability a. The system presents an absorbing state phase transition whenever the contamination probability a is above a minimum threshold. For short immunization times, the system evolves to a statistically stationary active state. Above τc(a), immunization predominates and the system evolves to the absorbing vacuum state. We employ a finite-size scaling analysis to show that the transition belongs to the standard directed percolation universality class. The critical immunization time diverges in the limit of a→1. In this regime, the density of active sites decays exponentially as τ increases, but never reaches the vacuum state in the thermodynamic limit.