The adenovirus vaccine and benzathine penicillin G (BPG) have been used by the US military to prevent acute respiratory diseases (ARD) in trainees, though these interventions have had documented manufacturing problems. We fit Poisson regression and random forest models (RF) to 26 years of weekly ARD incidence data to explore the impact of the adenovirus vaccine and BPG prophylaxis on respiratory disease burden. Adenovirus vaccine availability was among the most important predictors of ARD in the RF, while BPG was the ninth most important. BPG was a significant protective factor against ARD (incidence rate ratio (IRR) = 0.68; 95% confidence interval (CI) 0.67–0.70), but less so than either the old or new adenovirus vaccine (IRR = 0.39, 95% CI 0.38–0.39 and IRR = 0.11, 95% CI 0.11–0.11), respectively. These results suggest that BPG is moderately predictive of, and significantly protective against ARD, though to a lesser extent than either the old or new adenovirus vaccine.