A Differential Equation Model of Anxiety and Habituation Based on Allergic Responses and Its Computational Simulation Using Real-World Social Data

Abstract

We propose a mathematical model for the dynamics of anxiety that incorporates implicit habituation based on an analogy with allergic responses. Quantifying emotions such as anxiety remains challenging because objective information does not necessarily reflect people’s subjective anxiety. Anxiety also decreases when people are repeatedly exposed to similar information, a phenomenon analogous to immunotherapy for allergic responses. Our model incorporates the interaction between anxiety and implicit habituation based on this mechanism. We applied the model to anxiety related to the COVID-19 pandemic and successfully reproduced the reduced increase in anxiety under repeated exposure to similar stimuli. The proposed mathematical model provides a new perspective for understanding KANSEI dynamics.