This paper develops mathematical models for molecule harvesting transmitters in diffusive molecular communication (MC) systems. In particular, we consider a communication link consisting of a spherical transmitter nano-machine and a spherical receiver nano-machine suspended in a fluid environment. The transmitter and the receiver exchange information via signaling molecules. The transmitter is equipped with molecule harvesting units on its surface. Signaling molecules which come into contact with the harvesting units may be re-captured by the transmitter. For this system, we derive closed-form expressions for the channel impulse response and harvesting impulse response. Furthermore, we extend the harvesting transmitter model to the case of continuous signaling molecule release. In particular, we derive closed-form expressions for the average received signal at the receiver and the average harvested signal at the transmitter for different temporal release rates namely, constant, linearly increasing, and linearly decreasing release rates. Finally, we validate the accuracy of the derived mathematical expressions via particle-based simulations.