Brugada syndrome is a life-threatening genetic disorder of the heart’s electrical system, primarily caused by abnormalities in the function of ion channels, particularly sodium and potassium channels. This study aims to develop a flexible mathematical model to accurately represent the dynamics of cardiac action potentials and simulate the two main types of this condition. To achieve this, the Richards activation function—with a tunable shape parameter (h)—was employed instead of the standard logistic function across six classical electrophysiological models, including Hodgkin-Huxley, I_Nap+I_K, Ten Tusscher, Luo-Rudy, Beeler-Reuter, and Priebe-Beuckelman. Using the Particle Swarm Optimization (PSO) algorithm, the optimal value of h was extracted for each model under both normal and pathological conditions. Results showed that adjusting the parameter h can significantly restore key action potential features—namely amplitude (APA), duration (APD), and time to peak (t_peak)—toward physiological values. Notably, the Luo-Rudy and Priebe-Beuckelman models exhibited greater sensitivity to h variations, corresponding well with the electrophysiological patterns of Brugada types I and II. Sensitivity analysis further revealed that certain models respond more sharply to changes in the activation function, which may guide the selection of appropriate models for personalized simulation. The proposed model, without altering the core structure of ion channel equations, is capable of reconstructing genetic disturbances in cardiac electrophysiology by tuning a single key parameter. It offers strong potential for use in in-silico therapeutic design, arrhythmia risk assessment, and the development of patient-specific cardiac models.