  We study the effects of distinct types of quenched disorder in the contact
process (CP) with a competitive dynamics on bipartite sublattices. In the
model, the particle creation depends on its first and second neighbors and the
extinction increases according to the local density. The clean (without
disorder) model exhibits three phases: inactive (absorbing), active symmetric
and active asymmetric, where the latter exhibits distinct sublattice densities.
These phases are separated by continuous transitions; the phase diagram is
reentrant. By performing mean field analysis and Monte Carlo simulations we
show that symmetric disorder destroys the sublattice ordering and therefore the
active asymmetric phase is not present. On the other hand, for asymmetric
disorder (each sublattice presenting a distinct dilution rate) the phase
transition occurs between the absorbing and the active asymmetric phases. The
universality class of this transition is governed by the less disordered
sublattice.
