<p>Social media and streaming platforms have reshaped music consumption, enabling songs to go viral through social contagion processes that mirror the spread of infectious diseases. In this article, we investigate whether epidemiological models can effectively represent, interpret, and forecast music virality on online platforms. We introduce a wave-based approach that captures multiple independent bursts of popularity, which is not possible using classic epidemic models. We evaluate our approach using data from Spotify and TikTok, comparing its performance with traditional time-series forecasting methods. Our findings demonstrate that epidemic models are significantly more effective at capturing viral dynamics than long-term commercial success. In forecasting tasks, our method achieves accuracy comparable to conventional techniques, even when trained on partial data, while offering interpretable parameters that characterize diffusion speed, engagement duration, and adoption delay. A cross-platform comparison reveals that viral trajectories on TikTok are captured with even greater precision than those on Spotify. Overall, our findings support epidemic modeling as a powerful and interpretable framework for analyzing and forecasting music virality in contemporary digital ecosystems.</p>