Clinical trials are pivotal in cardiac drug development, yet they often fail due to inadequate efficacy and unexpected safety issues, leading to significant financial losses. Using in-silico trials to replace a part of physical clinical trials, e.g., leveraging advanced generative models to generate drug-influenced electrocardiograms (ECGs), seems an effective method to reduce financial risk and potential harm to trial participants. While existing generative models have demonstrated progress in ECG generation, they fall short in modeling drug reactions due to limited fidelity and inability to capture individualized drug response patterns. In this paper, we propose a Drug-Aware Diffusion Model (DADM), which could simulate individualized drug reactions while ensuring fidelity. To ensure fidelity, we construct a set of ordinary differential equations to provide external physical knowledge (EPK) of the realistic ECG morphology. The EPK is used to adaptively constrain the morphology of the generated ECGs through a dynamic cross-attention (DCA) mechanism. Furthermore, we propose an extension of ControlNet to incorporate demographic and drug data, simulating individual drug reactions. We compare DADM with the other eight state-of-the-art ECG generative models on two real-world databases covering 8 types of drug regimens. The results demonstrate that DADM can more accurately simulate drug-induced changes in ECGs, improving the accuracy by at least 5.79% and recall by 8%.