A neuronal population model of the sleep-wake switch is extended to incorporate impulsive external stimuli. The model includes the mutual inhibition of the sleep-active neurons in the hypothalamic ventrolateral preoptic area (VLPO) and the wake-active monoaminergic brainstem populations (MA), as well as circadian and homeostatic drives. Arbitrary stimuli are described in terms of their relative effects on the VLPO and MA nuclei and represent perturbations on the normal sleep-wake dynamics. By separating the model s intrinsic time scales, an analytic characterization of the dynamics in a reduced model space is developed. Using this representation, the model s response to stimuli is studied, including the latency to return to wake or sleep, or to elicit a transition between the two states. Since sensory stimuli are known to excite the MA, we correspondingly investigate the model s response to auditory tones during sleep, as in clinical sleep fragmentation studies. The arousal threshold is found to vary approximately linearly with the model s total sleep drive, which includes circadian and homeostatic components. This relationship is used to reproduce the clinically observed variation of the arousal threshold across the night, which rises to a maximum near the middle of the night and decreases thereafter. In a further application of the model, time-of-night arousal threshold and body temperature variations in an experimental sleep fragmentation study are replicated. It is proposed that the shift of the extrema of these curves to a greater magnitude later in the night is due to the homeostatic impact of the frequent nocturnal disturbances.