Optimizing Biomathematical Models of Fatigue for Predicting Performance in Military Operational Environments

Introduction: The demands of our modern “24/7” society predispose individuals to various consequences, including fatigue. Fatigue reduces alertness, negatively affecting quality of life, increasing accident rates, and decreasing work productivity. Biomathematical models of fatigue (BMMF) predict fatigue risk based on factors such as sleep history and time of day. Few studies have examined their application in military operational environments for predicting performance in tasks of varying difficulty. This study assessed the adequacy of a BMMF (2-B alert) in the training of special operations troops and its predictive value for marksmanship.

Methods: Twenty-six subjects were analyzed over five days under varying sleep conditions. The model's fit to alertness predictions was evaluated using the original parameters reported in the literature, as well as after applying non- linear optimizations (Nelder-Mead) with group data and individual data. Also, Bayesian learning (BL) and an Extended Kalman Filter (EKF) were used for a real-time, individual-level optimization. Finally, the model’s ability to predict performance in the marksmanship tests was assessed, including difficulty and fatigue prediction as fixed factors in a linear mixed-effects model.

Results: The original model had an RMSE of ~50ms for alertness predictions, while the other models showed RMSEs below 20ms. The EKF adjusted model explained 18% (p = 0.001) of marksmanship variance (task difficulty: 9%, p = 0.001; fatigue: 1%, p = 0.014). When categorizing the variables, it was observed that, under high task difficulty, a response time of more than 250 milliseconds was associated with poorer performance (AUC: 0.74 [0.68–0.80], Sensitivity: 0.72, Specificity: 0.68, Positive Predictive Value: 0.74, Negative Predictive Value: 0.66).

Conclusion: The main finding showed that optimizing the parameters based on field alertness tests provided more accurate predictions than using parameters reported in the literature. Additionally, we found that fatigue explained a small but significant proportion of the variance. Overall, these preliminary results will help in developing personalized strategies for managing fatigue and performance across different contexts.

Publication History

Article published online:
08 October 2025