This study explored a Bayesian belief networks (BBNs) approach, developing two distinct models for prioritizing the seven indicators related to the “rapid response to and mitigation of the spread of an epidemic” category within the context of both the specific category and the Global Health Security Index (GHS index). Utilizing data from the 2021 GHS index, the methodology involves rigorous preprocessing, the application of the augmented naive Bayes algorithm for structural learning, and k-fold cross-validation. Key findings show unique perspectives in both BBN models. In the mutual value of information analysis, “linking public health and security authorities” emerged as the key predictor for the “rapid response to and mitigation of the spread of an epidemic” category, while “emergency preparedness and response planning” assumed precedence for the GHS index. Sensitivity analysis highlighted the critical role of “emergency preparedness and response planning” and “linking public health and security authorities” in extreme performance states, with “access to communications infrastructure” and “trade and travel restrictions” exhibiting varied significance. The BBN models exhibit high predictive accuracy, achieving 83.3% and 82.3% accuracy for extreme states in “rapid response to and mitigation of the spread of an epidemic” and the GHS index, respectively. This study contributes to the literature on GHS by modeling the dependencies among various indicators of the rapid response dimension of the GHS index and highlighting their relative importance based on the mutual value of information and sensitivity analyses.