Modeling Disinformation Campaigns of Vaccine Fear Mongering and its Differential Game

Fear driven by misinformation and disinformation campaigns has serious consequences for public health. Rumors and falsehoods that threaten the safety of disease-control measures and undermine the integrity of healthcare systems can have lasting effects unless countered quickly and effectively. In this paper, we combine models of (mis)information, dynamic games, and mathematical epidemiology to examine how falsehoods influence vaccination acceptance, a crucial control measure for childhood diseases. The changing perceptions of fear and risk related to vaccines, driven by falsehoods spreading at varying intensities, shape vaccine uptake and, in turn, disease transmission. We introduce and analyze a differential game between disinformation and corrective campaigns to influence public opinion on vaccination. Competition between falsehoods and their rebuttals determines which narratives dominate, shaping collective risk perception and immunization behavior, a process we call informational competitive exclusion. By linking the information game to an epidemic transmission model, we identify equilibrium strategies and conditions under which timely, adaptive counter-messaging can reduce vaccine hesitancy and maintain vaccination coverage. Our results highlight critical thresholds and hysteresis in campaign strength that decide whether public confidence is restored or fear-driven hesitancy persists. These insights offer guidance for designing effective, adaptable public health communication strategies to combat coordinated disinformation efforts.