  The response of spatially extended systems to a force leading their steady
state out of equilibrium is strongly affected by the presence of disorder. We
focus on the mean velocity induced by a constant force applied on
one-dimensional interfaces. In the absence of disorder, the velocity is linear
in the force. In the presence of disorder, it is widely admitted, as well as
experimentally and numerically verified, that the velocity presents a stretched
exponential dependence in the force (the so-called 'creep law'), which is out
of reach of linear response, or more generically of direct perturbative
expansions at small force. In dimension one, there is no exact analytical
derivation of such a law, even from a theoretical physical point of view. We
propose an effective model with two degrees of freedom, constructed from the
full spatially extended model, that captures many aspects of the creep
phenomenology. It provides a justification of the creep law form of the
velocity-force characteristics, in a quasistatic approximation. It allows,
moreover, to capture the non-trivial effects of short-range correlations in the
disorder, which govern the low-temperature asymptotics. It enables us to
establish a phase diagram where the creep law manifests itself in the vicinity
of the origin in the force--system-size--temperature coordinates. Conjointly,
we characterise the crossover between the creep regime and a linear-response
regime that arises due to finite system size.
