  The critical behavior of the contact process (CP) in heterogeneous periodic
and weakly-disordered environments is investigated using the supercritical
series expansion and Monte Carlo (MC) simulations. Phase-separation lines and
critical exponents $\beta$ (from series expansion) and $\eta$ (from MC
simulations) are calculated. A general analytical expression for the locus of
critical points is suggested for the weak-disorder limit and confirmed by the
series expansion analysis and the MC simulations. Our results for the critical
exponents show that the CP in heterogeneous environments remains in the
directed percolation (DP) universality class, while for environments with
quenched disorder, the data are compatible with the scenario of continuously
changing critical exponents.
