We introduce an original mathematical model to analyze the diffusion of posts within a generic online social platform. Each user of such a platform has his own Wall and Newsfeed, as well as his own self-posting and re-posting activity. As a main result, using our developed model, we derive in closed form the probabilities that posts originating from a given user are found on the Wall and Newsfeed of any other. These probabilities are the solution of a linear system of equations. Conditions of existence of the solution are provided, and two ways of solving the system are proposed, one using matrix inversion and another using fixed-point iteration. Comparisons with simulations show the accuracy of our model and its robustness with respect to modeling assumptions related to user behavior. The novelty introduced by this article is that platform design and user activity (self- and re-posting) can be as important as the social graph structure when analyzing user influence in competing environments, and should always be taken into account.