Many studies have been made on diffusion in the field of epidemiology, and in the last few years, the development of social networking has induced new types of diffusion. In this paper, we focus on file diffusion on a peer-to-peer dynamic network using eDonkey protocol. On this network, we observe a linear behavior of the actual file diffusion. This result is interesting, because most diffusion models exhibit exponential behaviors. In this paper, we propose a new model of diffusion, based on the SI (Susceptible / Infected) model, which produces results close to the linear behavior of the observed diffusion. We then justify the linearity of this model, and we study its behavior in more details.