This letter presents a mathematical model that minimizes the number of wavelengths required for wavelength assignment in a wavelength-reusable multi-carrier-distributed (WRMD) wavelength division multiplexing mesh network. None of the source nodes in the WRMD network is equipped with laser diodes. It receives carrier wavelengths from a multi-carrier light source or reuses carrier wavelengths from other established lightpaths. The loop problem may occur in mesh topologies when a source node selects a reused carrier wavelength from a destination lightpath node, if we consider only flow conservation constraints, which are usually adopted in conventional network design. We solve the loop problem by formulating constraints that reflect the special characteristics of the WRMD network. To support the development of heuristic algorithms towards large-scale networks, our mathematical model, which can provide reference values including upper and lower bounds, is useful for benchmarks.