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.

To further study the issue of false information classification on social platforms after major emergencies, this study regards opinion leaders and Internet users as a false-information classification system and constructs three differential game models of decentralized, centralized, and subsidized decision-making based on optimal control and differential game theory. Comparison analyses and numerical simulations of optimal equilibrium strategies and the optimal benefit between opinion leaders and Internet users, the optimal trajectory and the steady-state value of the total volume of real information, and the optimal benefit of the false information clarification system are carried out. It is found that under centralized decision-making, equilibrium strategy and total benefit of opinion leaders and Internet users, system total benefit, and total volume of real information can achieve Pareto optimality. Although subsidized decision-making fails to achieve Pareto optimality, with opinion leaders providing cost subsidies for Internet users, it is possible to reach relative Pareto improvement compared with decentralized decision-making.

Digital transformation represents a strategic imperative for enterprises pursuing high-performance growth. This study selects A-share listed enterprises from 2014 to 2023 as the research sample and empirically examines the impact of digital transformation on enterprise risk-taking, as well as its internal transmission mechanisms, using a fixed effects model. The findings indicate that digital transformation has a significant positive effect on promoting enterprise risk-taking, particularly in state-owned enterprises and those with lower media attention. The director network and economic policy uncertainty positively moderate this relationship. Results from the mechanism analysis show that digital transformation enhances enterprise risk-taking through independent mediating channels that alleviate enterprises’ financing constraints and increase innovation investment, as well as through the chain mediation channel of “alleviating financing constraints → increasing innovation investment”. This research clarifies the specific mechanism underlying the impact of digital transformation on enterprise risk-taking and provides new evidence for understanding how digitalization enhances enterprise risk-taking by easing financing constraints and stimulating innovation. It holds important significance for helping enterprises improve their risk-taking capacity and promote sustainable development.