This study examines toxicity intensity’s impact on its spread using a variable control intervention model. By employing the SEIQR (Susceptible, Exposed, Infected, Quarantine, Recovery) epidemiological modeling, we analyze the propagation of toxicity intensities on social media. Datasets from two content areas on the X platform—the COVID-19 and social movements—are used to validate our model. We conducted the model sensitivity analysis using the Latin hypercube sampling-partial rank correlation coefficient method. The analysis reveals that some parameters positively affect the basic reproduction number \(\mathcal {R}_0\) , while others negatively affect it. The study finds that dividing data into moderate and high toxicity levels results in lower error rates compared to the model without intensity-based splitting. Based on these findings, specific intervention measures are recommended, offering theoretical support for designing effective online toxicity prevention and control strategies.