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Based on an analysis of kinetic processes in the continuous-wave (CW) single-wavelength two-photon pumped Rb-vapor laser (Rb-TPAL), a three-dimensional computational model is established using the rate equation. Based on the application of the model to cavity-enhanced Rb-TPAL [Yuan et al. , Optics Express 29, 4858 (2021)], the calculated and measured dependences of the laser power on the pump power show good agreement. We simulate the Rb-TPAL pumped by a high-power CW laser diode and analyze the effects of temperature, vapor cell length, pump waist, vapor cell transmission, and output mirror reflectance on the characteristics of the blue laser. The results suggest that the output power and efficiency of blue laser can be improved by optimizing the above parameters; however, the particles in the <inline-formula> <tex-math notation="LaTeX">5^{2}\text{D}_{5/2} </tex-math></inline-formula> level face difficulty to transition to the <inline-formula> <tex-math notation="LaTeX">6^{2}\text{P}_{3/2} </tex-math></inline-formula> level, and this limits the further improvement of blue laser efficiency; therefore, an approach is proposed to improve the efficiency of Rb-TPAL. This study can be useful for designing a two-photon pumped alkali metal laser with high-power output.