  We study the absorbing-state phase transition in the one-dimensional contact
process under the combined influence of spatial and temporal random disorders.
We focus on situations in which the spatial and temporal disorders decouple.
Couched in the language of epidemic spreading, this means that some spatial
regions are, at all times, more favorable than others for infections, and some
time periods are more favorable than others independent of spatial location. We
employ a generalized Harris criterion to discuss the stability of the directed
percolation universality class against such disorder. We then perform
large-scale Monte Carlo simulations to analyze the critical behavior in detail.
We also discuss how the Griffiths singularities that accompany the
nonequilibrium phase transition are affected by the simultaneous presence of
both disorders.
