© 2015 AIP Publishing LLC. According to previous reports, filamentary electron transport in resistive switching HfO2-based metal-insulator-metal structures can be modeled using a diode-like conduction mechanism with a series resistance. Taking the appropriate limits, the model allows simulating the high (HRS) and low (LRS) resistance states of the devices in terms of exponential and linear current-voltage relationships, respectively. In this letter, we show that this simple equivalent circuit approach can be extended to represent the progressive reset transition between the LRS and HRS if a generalized logistic growth model for the pre-exponential diode current factor is considered. In this regard, it is demonstrated here that a Verhulst logistic model does not provide accurate results. The reset dynamics is interpreted as the sequential deactivation of multiple conduction channels spanning the dielectric film. Fitting results for the current-voltage characteristics indicate that the voltage sweep rate only affects the deactivation rate of the filaments without altering the main features of the switching dynamics.