On modeling collective risk perception via opinion dynamics

Modeling the collective response to an emergency is a problem of paramount importance in social science and risk management. Here, we leverage the social psychology literature to develop a mathematical model tailored to such a real-world problem, grounded in the opinion dynamics theory. In our model, a network of individuals revise their risk perception by processing information broadcast by the institution and shared by peers, and accounts for heterogeneity in terms of individuals' trust in institutions, peers, and in their own risk sensitivity. Through a rigorous analysis of the model, we establish that the temporal average opinions of the individuals converge to a steady state and, under some assumptions, we are able to analytically characterize such a steady state, shedding light on how the individuals' heterogeneous risk sensitivity shapes the collective response. Numerical results and simulations are provided to illustrate and corroborate our findings.