Caffeine is the most widely consumed stimulant to counter sleep-loss effects. While the pharmacokinetics of
caffeine in the body is well-understood, its alertness-restoring effects are still not well characterized. In fact, mathematical models capable of predicting the effects of varying doses of
caffeine on objective measures of vigilance are not available. In this paper, we describe a phenomenological model of the dose-dependent effects of
caffeine on psychomotor vigilance task (PVT) performance of sleep-deprived subjects. We used the two-process model of sleep regulation to quantify performance during sleep loss in the absence of
caffeine and a dose-dependent multiplier factor derived from the Hill equation to model the effects of single and repeated
caffeine doses. We developed and validated the model fits and predictions on PVT lapse (number of reaction times exceeding 500 ms) data from two separate laboratory studies. At the population-average level, the model captured the effects of a range of
caffeine doses (50-300 mg), yielding up to a 90% improvement over the two-process model. Individual-specific
caffeine models, on average, predicted the effects up to 23% better than population-average
caffeine models. The proposed model serves as a useful tool for predicting the dose-dependent effects of
caffeine on the PVT performance of sleep-deprived subjects and, therefore, can be used for determining
caffeine doses that optimize the timing and duration of peak performance.