<p>This paper investigates the optimal public strategies to mitigate the spread of fake news by integrating education and fact-checking into a behavioral compartmental model. Building on an SVIR framework, we incorporate endogenous learning and reputational feedback, while explicitly modeling super-spreaders who disproportionately amplify misinformation. We formulate a dynamic optimal control problem in which the government chooses the optimal investment rate in education and fact-checking to minimize societal costs, which include the vulnerable population, reputational penalties, and the economic costs of interventions. Numerical simulations illustrate the interplay between learning, super-spreader dynamics, and public interventions, highlighting how targeted educational policies can effectively reduce misinformation diffusion and optimize resource allocation for long-term societal benefits. The results offer both theoretical and practical insights into designing policies to combat the viral spread of fake news in the digital age.</p>