The wide adoption of social media has increased the interaction among different pieces of information, and this interaction includes cooperation and competition for our finite attention. While previous research focus on fully competition, this paper extends the interaction to be both "cooperation" and "competition", by employing an IS1S2 R model. To explore how two different pieces of information interact with each other, the IS1S2 R model splits the agents into four parts-(Ignorant-Spreader I-Spreader II-Stifler), based on SIR epidemic spreading model. Using real data from Weibo.com, a social network site similar to Twitter, we find some parameters, like decaying rates, can both influence the cooperative diffusion process and the competitive process, while other parameters, like infectious rates only have influence on the competitive diffusion process. Besides, the parameters' effect are more significant in the competitive diffusion than in the cooperative diffusion.