Although official departments attempt to intervene against misinformation, the personal field often conflicts with the goals of these departments. Thus, when rumours spread widely on social media, decision-makers often use a combination of rigid and soft control measures, such as blocking keywords, deleting misinformation, suspending accounts or refuting misinformation, to decrease the diffusion of misinformation. However, existing methods rarely consider the interplay of blocking and rebuttal measures, resulting in an unclear effect of the double intervention mechanism. To address these issues, we propose a novel misinformation diffusion model called SEIRI (susceptible, exposed, infective, removed, and infective) that considers the double intervention mechanism and secondary diffusion characteristics. We analyse the stability of the proposed model, obtain rumour-free and rumour-spread equilibriums, and calculate the basic reproduction number. Furthermore, we conduct numerical simulations to analyse the influence of key parameters through comparative experiments. Finally, we validate the effectiveness of the proposed approach by crawling a real-world data set of COVID-19-related misinformation tweets from Sina Weibo. Our comparison experiments with other similar works show that the SEIRI model provides superior performance in characterising the actual spread of misinformation. Our findings lead to several practical implications for public health policymaking.