Fake health-related news has spread rapidly through the internet, causing harm to individuals and society. Despite interventions, a fenbendazole scandal recently spread among patients with lung cancer in South Korea. It is crucial to intervene appropriately to prevent the spread of fake news. This study investigated the appropriate timing of interventions to minimize the side effects of fake news. A simulation was conducted using the susceptible-infected-recovered (SIR) model, which is a representative model of the virus spread mechanism. We applied this model to the fake news spread mechanism. The parameters were set similarly to those in the digital environment, where the fenbendazole scandal occurred. NetLogo, an agent-based model, was used as the analytical tool. Fake news lasted 278 days in the absence of interventions. As a result of adjusting and analyzing the timing of the intervention in response to the fenbendazole scandal, we found that faster intervention leads to a shorter duration of fake news (intervention at 54 days = fake news that lasted for 210 days; intervention at 16 days = fake news that lasted for 187 days; and intervention at 10 days = fake news that lasted for 157 days). However, no significant differences were observed when the intervention was performed within 10 days. Interventions implemented within 10 days were effective in reducing the duration of the spread of fake news. Our findings suggest that timely intervention is critical for preventing the spread of fake news in the digital environment. Additionally, a monitoring system that can detect fake news should be developed for a rapid response.