Two-stage predictions of evolutionary dynamics during the rumor dissemination

The spreading of rumor is the common type of collective actions. As a macro social phenomenon, the rumor spreading should be supported by the micro-level actions and interactions of people (agents). Therefore, the agent-based modeling is applied to modeling the micro-level mechanism of rumor spreading, which has more significance in the big data age. The outcomes of simulations indicate that there exist a stage transfer and the turning point D, which divides the whole spreading process into the linear (OD) and nonlinear (DE) stages. In the linear stage OD, the spreading percentage increases rapidly into a relatively high level of spreading percentage. However, after the turning point D, it increases slowly until the 100% is reached in the nonlinear stage DE. For the linear stage OD, we estimated the linear dynamics with the linear OLS regression, and it suggests that the adjusted R2 is as high as over 98%–99%, which is infinitely close to 100%; for the nonlinear stage DE, we estimated the nonlinear stage via adding the quadratic term of time into the regression model. It suggests that the adjusted R2 is as high as over 98% as well, which is also close to 100%. Based on the predictions of linear and nonlinear stages with the highest accuracies, we combined the linear and nonlinear stages (OE=OD+DE) to predict the whole process of rumor spreading. Eventually, the Smooth Predicted Curves (SPCs) can be obtained to better fit the evolutionary dynamic of spreading curves in reality.