In order to understand the message propagation performance in Mobile ad-hoc Networks (MANETs), various methods and models have been proposed in the literature by applying a common pairwise meeting rate between mobile nodes. In this paper, based on this classical meeting rate, we develop an Ordinary Differential Equations (ODEs) based analytical framework aiming at depicting the propagation process of a target message while using a controlled epidemic routing protocol. Each relay node is assigned a threshold value of its buffer can be occupied by the target message copies in such the controlled epidemic routing. Further, we also investigate the effect of the threshold to the total buffer occupancy ratio over all the relay nodes using our proposed theoretical framework. The correctness of our analysis is validated by extensive simulations.