The prediction of evacuation demand curves is a crucial step in the disaster evacuation plan making, which directly affects the performance of the disaster evacuation. In this paper, we discuss the factors influencing individual evacuation decision making (whether and when to leave) and summarize them into four kinds: individual characteristics, social influence, geographic location, and warning degree. In the view of social contagion of decision making, a method based on Susceptible-Infective (SI) model is proposed to formulize the disaster evacuation demand curves to address both social influence and other factors’ effects. The disaster event of the “Tianjin Explosions” is used as a case study to illustrate the modeling results influenced by the four factors and perform the sensitivity analyses of the key parameters of the model. Some interesting phenomena are found and discussed, which is meaningful for authorities to make specific evacuation plans. For example, due to the lower social influence in isolated communities, extra actions might be taken to accelerate evacuation process in those communities.