Modeling and dynamic behaviors of the second wave of social media-based public opinion with a case study

In the social media age, the multi-stage communication has progressively developed into the predominant mode of online information dissemination. To our best knowledge, a dearth of studies concern the second outbreak of social media-based public opinion. Hence in the paper, a mathematical model is proposed by a system of ordinary differential equations to analyze the dynamic behaviors of the second wave of public opinion. The basic reproduction number R0 is a sharp threshold, in the sense that when R0≤1, the public-opinion-free equilibrium is asymptotically stable, and then the second wave of public discourse eventually disappears; while when R0>1, the public-opinion-existence equilibrium is asymptotically stable, and hence the second wave of public opinion is always persistent within a population. With the data from the “BMW Mini ice cream event”, the case-specific parameters are determined to validate our model by comparing the simulated curve with the real world data. Numerical simulations are implemented to illustrate the feasibility of the theoretical results. This paper provides novel insights to cyber information security, including establishing control strategies to contain the public-opinion second outbreak, measuring the popularity level of the public-opinion second wave by the final scale of its Spreaders, and assessing the population of the silent majority who keep silent but serve as underlying drivers for propagating public discourse.