Information regarding vaccines from sources such as health services, media, and social networks can significantly shape vaccination decisions. In particular, the dissemination of negative information can contribute to vaccine hesitancy, thereby exacerbating infectious disease outbreaks. This study investigates strategies to mitigate anti-vaccine social contagion through effective counter-campaigns that disseminate positive vaccine information and encourage vaccine uptake, aiming to reduce the size of epidemics. In a coupled agent-based model that consists of opinion and disease diffusion processes, we explore and compare different heuristics to design positive campaigns based on the network structure and local presence of negative vaccine attitudes. We examine two campaigning regimes: a static regime with a fixed set of targets, and a dynamic regime in which targets can be updated over time. We demonstrate that strategic targeting and engagement with the dynamics of anti-vaccine influence diffusion in the network can effectively mitigate the spread of anti-vaccine sentiment, thereby reducing the epidemic size. However, the effectiveness of the campaigns differs across different targeting strategies and is impacted by a range of factors. We find that the primary advantage of static campaigns lies in their capacity to act as an obstacle, preventing the clustering of emerging anti-vaccine communities, thereby resulting in smaller and unconnected anti-vaccine groups. On the other hand, dynamic campaigns reach a broader segment of the population and adapt to the evolution of anti-vaccine diffusion, not only protecting susceptible agents from negative influence but also fostering positive propagation within negative regions.