This paper presents a physics-based analytical model for investigating charge trapping in GaN high-electron-mobility transistors (HEMTs), using the École Polytechnique Fédérale de Lausanne HEMT core model. It introduces a realistic continuous density of interface traps, distributed across the upper half of the gallium nitride bandgap with an exponential tail function, differing from traditional discrete energy levels. The model's accuracy is confirmed through alignment with technology computer-aided design simulations and experimental data from a practical HEMT. Validation also includes comparing transfer and output characteristics against experimental results of an AlGaN/GaN device. This work lays the groundwork for a compact model that addresses interface-trap-induced degradation in GaN HEMT performance.