We have constructed a line-by-line model of the A-X system of CO in order to analyze the CO bands appearing in the UV spectra of comets. The model includes electronic, rotational, vibrational transitions, excitations by solar UV radiation, and effects of neutral and electron collisions. The major bands of the A-X system occur in the $1200 - 1800{AA}$ range where the temporal variation of solar irradiation is significant. The solar spectrum in this spectral range shows many emission lines, which cause a significant Swings effect. We derived fluorescence efficiencies of the bands as functions of heliocentric velocity and cometocentric distance using a high resolution spectrum of the sun. We compared our model with a spectrum of comet P/Halley obtained with the IUE, and estimated that the UV Swings effects are less than 20 fluorescence efficiencies for the most bands of the A-X system. We discuss the temporal variation of solar UV irradiation and its effects on the fluorescence efficiencies. The study of the A-X system also requites knowledge of vibrational and rotational fluorescent processes in the infrared and radio regions because the majority of CO molecules in the coma is in the ground rotational states. The solar infrared spectrum near 5 microns, where the fundamental band of CO occurs, contains strong absorption lines of the fundamental band and hot bands of CO and its isotopes. We derived fluorescence efficiencies of the infrared band as functions of heliocentric velocity and cometrocentric distance. The solar absorption lines near 5 microns cause a 20 reduction of the g-factor of the fundamental band at heliocentric velocities close to 0 km/sec. We discuss the effects of neutral and electron collisions on the fluorescence efficiencies of the infrared and UV bands.