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Dynamic metasurface antennas (DMAs) arise as a promising technology in the field of massive multiple-input multiple-output (mMIMO) systems, offering the possibility of integrating a large number of antennas in a limited -- and potentially large -- aperture while keeping the required number of radio-frequency (RF) chains under control. Although envisioned as practical realizations of mMIMO systems, DMAs represent a new paradigm in the design of signal processing techniques (such as beamforming) due to the constraints inherent to their physical implementation, for which no complete models are available yet. In this work, we propose a complete and electromagnetic-compliant narrowband communication model for a generic DMA based system. Specifically, the model accounts for: i) the wave propagation and reflections throughout the waveguides that feed the antenna elements, ii) the mutual coupling both through the air and the waveguides, and iii) the insertion losses. Also, we integrate the electromagnetic model in the conventional digital communication model, providing a complete and useful framework to design and characterize the performance of these systems. Finally, the accuracy of the model is verified through full-wave simulations.