USEIRS model for the contagion of individual aggressive behavior under emergencies

Individual aggressive behavior under emergencies is contagious, and often leads to collective aggressive behavior. In this paper, we apply the epidemic model to investigate the contagion of individual aggressive behavior under emergencies, extending the SEIRS (Susceptible–Exposed–Infected–Recovered–Susceptible) model by adding a new group of people – uninducible individuals. Thus, a new dynamic model USEIRS (Uninducible–Susceptible–Exposed–Infected–Recovered–Susceptible) is developed. The threshold of individual aggressive behavior contagion is deduced from the USEIRS model through the analysis of the eliminating and prevailing stabilities and equilibrium of aggressive behavior contagion. The numerical solutions of the USEIRS model show that a higher number of initial uninducible individuals can reduce the number of people with aggressive behavior. However, the decrease in the number of aggressive individuals will be insignificant if the uninducible individuals have little influence on the public. A higher uninducible rate can reduce the number of individuals with aggressive behavior. However, some people will still inevitably behave aggressively at the beginning. The effect of higher uninducible rate has an accelerating feature, which becomes more obvious with the development of emergency. Providing information and education to increase the uninducible population, or more communication between experts, government officials and the general public to increase the uninducible rate are strategies for reducing individual aggressive behavior.