This paper proposes a novel imperfect transmitter (TX) model, namely the membrane fusion (MF)-based TX, that adopts MF between a vesicle and the TX membrane to release molecules encapsulated within the vesicle. For the MF-based TX, the molecule release probability and the fraction of molecules released from the TX membrane are derived. Incorporating molecular degradation and a fully-absorbing receiver (RX), the channel impulse response (CIR) is derived for two scenarios: 1) Both TX and RX are static, and 2) both TX and RX are diffusion-based mobile. Moreover, a sequence of bits transmitted from the TX to the RX is considered. The average bit error rate (BER) is obtained for both scenarios, wherein the probability mass function (PMF) of the number of molecules absorbed in the mobile scenario is derived. Furthermore, a simulation framework is proposed for the MF-based TX, based on which the derived analytical expressions are validated. Simulation results show that a low MF probability or low vesicle mobility slows the release of molecules and reduces the molecule hitting probability at the RX. Simulation results also indicate the difference between the MF-based TX and an ideal point TX in terms of the inter-symbol interference (ISI).