Fatigue risk in humans has few biomathematical models, and existing biomathematical models have many shortcomings. We developed a biomathematical model of fatigue risk based on the concept of energy to quantify human alertness from the perspective of energy and used alertness to characterise human psychological fatigue risk. The model allows mathematical modelling of activity processes that concern sleep intensity and quality and distinguishes between intrinsic exertion in the waking state and workload exertion in the workload state. This alertness and fatigue risk biomathematical model predicts changes in human alertness and fatigue risk indices at any point in the day. We applied numerical simulation and model analysis to five cases to validate the potential value of the alertness energy fatigue risk biomathematical model. Practitioner summary: To overcome the shortcomings of current biomathematical models that evaluate fatigue risk, this study developed a biomathematical model of fatigue risk based on the concept of energy to quantify human alertness from the perspective of energy and used alertness to characterise human fatigue risk. Abbreviations : S: The sleep homeostatic process; C: The circadian process; SAFTE: The sleep activity fatigue and task effectiveness model; FAID: The fatigue audit interdyne model; EEG: Electroencephalogram.