Mathematical modeling of human behaviors during catastrophic events.

International audienceIn 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 mathematical model taking into account different concurrent behaviors in such situation and to include the processes of transition 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 propose a SIR-based model, where three types of collective reactions occur in catastrophe situations: reflex, panic and controlled behaviors. Moreover, we suppose that the interactions among these classes of population can be realized through imitation and emotional contagion processes. Some simulations will attest the relevance of the proposed model