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We modeled the response of superconducting nanowire single-photon detectors during a photodetection event, taking into consideration only the thermal and electrical properties of a superconducting NbN nanowire on a sapphire substrate. Our calculations suggest that heating which occurs after the formation of a photo-induced resistive barrier is responsible for the generation of a measurable voltage pulse. We compared this numerical result with experimental data of a voltage pulse from a slow device, i.e. large kinetic inductance, and obtained a good fit. Using this electro-thermal model, we estimated the temperature rise and the resistance buildup in the nanowire, and the return current at which the nanowire becomes superconducting again. We also show that the reset time of these photodetectors can be decreased by the addition of a series resistance and provide supporting experimental data. Finally we present preliminary results on a detector latching behavior that can also be explained using the electro-thermal model.