[en] A simplified model of the interaction between ''quarks'' and ''gluons'' with the infrared asymptotics of the gluon propagator is considered. The requirement of a consistent description of ''gluon'' and ''quark'' propagators and a vertex function is shown to lead, in the particular covariant gauge, to an eigenvalue problem for the ''magnetic moment'' and the mass of the ''quark''. This eigenvalue problem has a unique solution in the model. The considered simplified theory can be interpreted as a model which describes qualitatively the situation in the infrared region for QSD