The hollow-core fiber gas laser (HCFGL) has developed into a significant mid-infrared laser source, but the development of theoretical model still lags behind experimental progress. In this work, we propose a multi-level vibrational thermal pool (VTP) model of HBr-filled HCFs, which comprehensively considers the rovibrational relaxation effects on laser gain in reasonable approximations of transition coefficients, and studies the laser characteristics on multi-line lasing, bottleneck effect, line competition, etc. The VTP model shows more precise results of laser slope efficiency, and threshold than previous models while fitting the experimental data very well, and successfully predicts an output bottleneck at 1 W pump. The P-branch laser is relatively advantageous over the R-branch laser for its larger Einstein $A$ coefficient and emission cross section, and the seed injection can intensify the line competition and reach the highest P4 power proportion of 80%. The VTP model reveals that the output of various pump lines has a pattern similar to the Boltzmann distribution, suggesting that the distribution of ground rotational levels limits the laser gain of pump lines. Moreover, we discuss the photon leakage in high-energy pulsed pumping conditions. With the introduction of the leaking coefficient, this model shows relaxation oscillations and laser slope efficiencies close to experimental values and greater than the results in the CW condition, and solves the overpump problem in pulsed pump simulation. Finally, we confirm that the photon leakage is intensified at high repetition rate and the leaking coefficient should relate to the pulse repetition rate. This work develops a comprehensive modeling method for MIR laser simulation and this model is also applicable to various gas-filled HCFGLs.