The possible mutual influence and synergistic effect between defect production and the presence of hydrogen isotopes in the crystal lattice of tungsten is studied. For this purpose, we perform modeling of experimental data where polycrystalline tungsten samples were in one case sequentially irradiated by 10.8 MeV tungsten ions followed by low-energy deuterium exposure and in the other case simultaneously irradiated by tungsten ions, while exposed to deuterium atoms. Modeling of the measured deuterium depth profiles and thermal-desorption spectra for different irradiation temperatures is performed by the MHIMS (migration of hydrogen isotopes in materials) code. A model of trap creation due to tungsten ion irradiation during the deuterium atom exposures is implemented. In both experimental series, the deuterium desorption peaks corresponding to defects induced by tungsten irradiation are described by the same two de-trapping energies of 1.83 and 2.10 eV. The experiments give unambiguous proof that the presence of deuterium increases the overall trap density. The modeling reveals that the two trap concentrations are affected differently by the temperature and presence of deuterium: the concentration of the low-energy trap is significantly higher in the case of simultaneous exposure compared to sequential exposure, especially at high temperature (2.2 times higher at 1000 K). The concentration of the high-energy trap is only weakly affected by the presence of hydrogen.