Biomathematical models of fatigue capture the physiology of sleep/wake regulation and circadian rhythmicity to predict changes in neurobehavioral functioning over time. We used a biomathematical model of fatigue linked to the adenosinergic neuromodulator/receptor system in the brain as a framework to predict sleep inertia, that is, the transient neurobehavioral impairment experienced immediately after awakening. Based on evidence of an adenosinergic basis for sleep inertia, we expanded the biomathematical model with novel differential equations to predict the propensity for sleep inertia during sleep and its manifestation after awakening. Using datasets from large laboratory studies of sleep loss and circadian misalignment, we calibrated the model by fitting just two new parameters and then validated the model’s predictions against independent data. The expanded model was found to predict the magnitude and time course of sleep inertia with generally high accuracy. Analysis of the model’s dynamics revealed a bifurcation in the predicted manifestation of sleep inertia in sustained sleep restriction paradigms, which reflects the observed escalation of the magnitude of sleep inertia in scenarios with sleep restriction to less than ∼ 4 h per day. Another emergent property of the model involves a rapid increase in the predicted propensity for sleep inertia in the early part of sleep followed by a gradual decline in the later part of the sleep period, which matches what would be expected based on the adenosinergic regulation of non-rapid eye movement (NREM) sleep and its known influence on sleep inertia. These dynamic behaviors provide confidence in the validity of our approach and underscore the predictive potential of the model. The expanded model provides a useful tool for predicting sleep inertia and managing impairment in 24/7 settings where people may need to perform critical tasks immediately after awakening, such as on-demand operations in safety and security, emergency response, and health care.