A simple, semi-analytical model of diode pumped alkali lasers (DPALs), applicable to both static and flowing-gas devices, is reported. Unlike other models, assuming a 3-level scheme of the laser and neglecting influence of the temperature on the lasing power, it takes into account temperature rise and losses of alkali atoms due to ionization and chemical reactions, resulting in a decrease of the pump absorption and slope efficiency. The applicability of the model is demonstrated by (1) obtaining good agreement with measurements in a static DPAL [B.V. Zhdanov, J. Sell and R.J. Knize, Electron. Lett. 44, 582 (2008)], (2) predicting the dependence of power on the flow velocity in flowing-gas DPALs and (3) checking the effect of using a buffer gas with high molar heat capacity and large relaxation rate constant between the 2 P 3/2 and 2 P 1/2 fine-structure levels of the of the alkali atom. It is found that ionization processes have a small effect on the laser operation, whereas chemical reactions of alkali atoms with hydrocarbons strongly affect the lasing power. The power strongly increases with flow velocity and by replacing, e.g., ethane by propane as a buffer gas the power may be further increased by up to 30%. 8 kW is achievable for 20 kW pump at flow velocity of 20 m/s.