Abstract
Emotion plays an important role in decision making. In an emergency, panic can spread among crowds through person-to-person communications and can cause harmful effects on society. The aim of this paper is to propose a new theoretical model in the context of epidemiology to describe the spread of panic under an emergency. First, according to divisions in personality in the context of psychology, groups are divided into a level-headed group and an impatient group. Second, individuals in the two groups have unique personalities. Thus, the level-headed group only infects within the group, while the impatient group considers emotional infection within the group and cross infection between the groups. Then, a nonlinear infection rate is used to describe the probability of infection after an infected person contacts a susceptible person, which is more in line with the real situation. After that, the level-headed group–impatient group nonlinear SIRS panic spreading model is developed. Stable analysis of the model is obtained using the Lyapunov function method to study the stability of the panic-free equilibrium and panic-permanence equilibrium. Finally, simulations are carried out to dynamically describe the spread process of group emotional contagion.
Highlights
In recent years, public safety emergencies, such as fires, earthquakes, and stampedes have occurred frequently, which have led to public panic and caused a certain psychological burden on people [1]
Group emotional contagion is a process of mutual spread between individuals, which is similar to the process of virus transmission in the epidemiology model [20]
Model and the susceptible-infected-recovered (SIR) model [21,22,23]. On this basis, combining a knowledge of psychology and sociology, these were applied to emotion modeling, which simulated the psychological state of individuals under an emergency, and widely used in the field of emotion contagion [24,25,26,27,28,29,30,31]
Summary
Public safety emergencies, such as fires, earthquakes, and stampedes have occurred frequently, which have led to public panic and caused a certain psychological burden on people [1]. Group emotional contagion is a process of mutual spread between individuals, which is similar to the process of virus transmission in the epidemiology model [20]. Model and the susceptible-infected-recovered (SIR) model [21,22,23] On this basis, combining a knowledge of psychology and sociology, these were applied to emotion modeling, which simulated the psychological state of individuals under an emergency, and widely used in the field of emotion contagion [24,25,26,27,28,29,30,31].
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