Organic electrochemical transistors (OECTs) are a class of promising neuromorphic devices due to their exceptional conductivity, ease of fabrication, and cost-effectiveness. These devices exhibit ionic behavior similar to biological synapses, enabling efficient switching. Developing a compact model for OECTs is challenging due to the complex interplay of electrochemical reactions, ion transport, interactions with electrons or holes, and charge carrier dynamics that must be accurately captured and integrated into a simplified framework. In this work, we develop a combined physics-based compact model that integrates the Nernst equation from electrochemistry with thermally activated charges from semiconductor physics. This model enables easy incorporation into circuit simulations and provides a simple core framework for further extensions to account for additional effects. We fabricated, characterized, and analyzed OECTs based on PEDOT:PSS, and the proposed compact model shows good agreement with our experimental data.