MATHEMATICAL MODELING OF HUMAN BEHAVIORS DURING CATASTROPHIC EVENTS.

Abstract. In this paper, we introduce a new approach for modeling the human collective behaviors in the specific scenario of a sudden catastrophe, this catastrophe can be natural (i.e. earthquake, tsunami) or technological (nuclear event). The novelty of our work is to propose a mathemat-ical model taking into account different concurrent behav-iors in such situation and to include the processes of transi-tion from one behavior to the other during the event. Thus, in this multidisciplinary research included mathematicians, computer scientists and geographers, we take into account the psychological reactions of the population in situations of disasters, and study their propagation mode. We pro-pose a SIR-based model, where three types of collective re-actions occur in catastrophe situations: reflex, panic and controlled behaviors. Moreover, we suppose that the inter-actions among these classes of population can be realized through imitation and emotional contagion processes. Some simulations will attest the relevance of the proposed model