Analysis of a New Mathematical Model for Epidemic Fear Propagation Under Media Influence

Abstract Recent global epidemics have triggered widespread negative emotions such as anxiety, fear, and anger. Understanding the dynamics of epidemic-related fear has therefore become a crucial aspect of public health research. This study proposes a new social mathematical model to investigate the epidemic-related fear propagation dynamics within a population. In the model, people are divided into five psychological states based on their fear status and awareness level: susceptible, aware, exposed, fearful, and recovered. Additionally, fear propagates among exposed and fearful people through terrible news in the media. The basic reproduction number is calculated in association with exposed and fearful people and terrible news. The sensitivity of this threshold parameter is analyzed with respect to the model parameters. The local and global stability of the proposed fear propagation model is discussed at the fear-free and endemic equilibrium points. The model parameters are hypothesized based on existing studies on COVID-19 fear in Turkey, and numerical simulations are presented accordingly. The results show that fear propagation behavior is exacerbated by loss of awareness and direct interpersonal interaction with exposed and fearful people, as well as indirect contact with terrible news in media. Under the influence of fear, people are concentrated in the fearful compartment and interact with susceptible and aware compartments, affecting the overall behavior of fear propagation dynamics. These findings highlight the critical role of psychological factors, particularly fear, in shaping behavioral responses during epidemics and underscore the need for targeted public health interventions that address both direct interpersonal interaction and indirect media-influenced fear propagation.