A critical review of existing mathematical models for alertness

Existing biomathematical models of human fatigue and performance are reviewed with the aim of identifying open questions and ways of improving models. Most fatigue and alertness models are based on the twoprocess model of sleep regulation. They present a mathematical formulation of the two-process model targeted on different metrics including alertness, fatigue, sleepiness, performance measures and accident risk. One of the reviewed fatigue models is completely empirical without reference to sleep regulation. Differences between the models result from the specific data set on which a model is based. These data sets determine the possible application areas for the models ranging from airline operations, car and truck drivers to industrial shift work. It is generally accepted that fatigue models are useful also for educating people about fatigue in non-standard work situations and for generating scientific hypotheses that can be tested by experiments. Important points for the improvement of models include the consideration of cumulative fatigue, interindividual differences, effects of external factors such as light on fatigue, and task-related effects. Very few models consider the task-related fatiguing effect of different activities.