Computational models and optimal control strategies for emotion contagion in the human population in emergencies

Emotions play an important role in the decision-making of individuals. Emotional contagion has an influence on individual and group-level behaviors. Particularly, the contagion of negative emotions like panic emotions may result in devastating consequences in the human population in emergencies. This work develops novel computational models of emotion contagion and solves the optimal control problem of emotion contagion in the human population in emergencies. Firstly, by introducing a concept of latent state and considering complicated interactions among individuals, we develop a novel conceptual model of emotion contagion, and further establish a computational model for describing the dynamics of emotion contagion, called the susceptible-latent-infectious-recovered-susceptible (SLIRS) model. Secondly, by considering vaccination, quarantine and treatment as control measures, we expand the SLIRS model into a controlled SLIRS model, and formulate the control problem of emotion contagion as an optimal control problem, so that the total costs of inhibiting emotion contagion are minimized. Finally, we theoretically discuss the existence and uniqueness of the solution of the controlled SLIRS model, and further derive an optimal control solution of the controlled SLIRS model. The simulation results on the synthesis dataset and the real trace dataset show that the optimal control strategies have significant impact on emotion contagion. Especially, the optimal control strategy with a mixture of vaccination, quarantine and treatment can significantly decrease the scale of the outbreak of negative emotions, and incur the lowest total costs of inhibiting emotion contagion. This enables the optimal decision-making for inhibiting emotion contagion under the consideration of limited resources in the human population in emergencies. Hence, this work will make contributions to crisis management and crowd evacuation in emergencies.