A mathematical model for the diffusion of emergency warning messages during CBRNe emergencies

Understanding the diffusion of warning messages is essential to adequately respond to emergency events and situations. This is especially true in urgent scenarios, that is situations where external events are happening at the same rate or faster than the diffusion process itself. In this paper, an information diffusion model (Bass model) is proposed to study the spread of warning messages during emergencies involving urgent diffusion dynamics, for example a CBRNe event. In the present study, the Bass model is applied to two hazardous materials transportation accidents reported in the literature: the Pittsburgh phosphorus oxychloride release and the precautionary evacuation occurred in Confluence due to toxic chemicals released after a train derailment. Warning data collected from the two accidents and reported in published literature studies were used in this work and fitted with the Bass model. The diffusion of emergency warning messages is modelled as a two‐component system, where the spread of information is characterized by (a) a “broadcast process” that disseminates the emergency warning vertically (in the sense that many people are alerted simultaneously) and (b) a horizontal “contagion process” whereby people first hear of the event and then sequentially tell others (social media, word‐of‐mouth and peer‐to‐peer communication). The Bass model provided an excellent fit of the warning diffusion times related to both accidents suggesting that the very first phase of the warning process is sustained by a “broadcast” information diffusion process. However, after less than 1 hr from the beginning of the warning process the efficacy of its diffusion is dominated by the “contagion” component, that is the effectiveness of a robust social network between individuals. In conclusion, the Bass model proved to be a handy tool to assess epidemics spreading of information from the people who adopted the information. Our results suggest that the general Bass model applied to diffusion of emergency warning has the potential to provide key information in the management of emergencies. This approach can be applied right away by professional communicators, advisors and decision‐makers in case of a CBRNe event.