Background: Burnout affects approximately 37-56% of medical undergraduates globally, escalating to around 44% immediately prior to residency and posing a substantial threat to healthcare workforce sustainability.Methods: This theoretical manuscript introduces a hybrid modeling framework that integrates a deterministic Susceptible-Infected-Recovered-Susceptible (SIRS) model of burnout contagion with Bayesian hierarchical inference for risk factor analysis, informed by meta-analytic priors. Key calibrated parameters encompass the initial prevalence 0.3723, weekly transmission rate 0.05 (derived from longitudinal escalation patterns), recovery rate 0.02 (reflecting mindfulness intervention effects, standardized mean difference = -0.42), and relapse rate 0.01. Hierarchical priors incorporate empathy-burnout correlations (effect size r = -0.15) and stress-related coefficients (0.39). Markov chain Monte Carlo (MCMC) posteriors, based on 10,000 iterations, are estimated. Sensitivity analysis via parameter sweeps and Monte Carlo simulations (with parameters drawn from normal distributions: \( \beta \sim \mathcal{N}(0.05, 0.005) \), \( \gamma \sim \mathcal{N}(0.02, 0.002) \), \( \delta \sim \mathcal{N}(0.01, 0.001) \)) are performed.Results: Sensitivity analysis demonstrates that variations in stress levels and transmission rates significantly influence peak burnout prevalence, with posteriors estimating stress coefficient 0.40 (95% highest density interval: 0.35--0.45) and empathy -0.16 (95% highest density interval: -0.21-- -0.11). Parameter sweeps attribute 85% of peak prevalence variance to transmission rate, while Monte Carlo simulations yield 95% prediction intervals of 380--485 cases for a cohort of 1000. Posterior predictive checks (p = 0.07) validate model fit to observed empirical peaks (45% in year 3). Projected interventions, such as pass/fail grading (odds ratio = 1.4, modeled as \( \beta \to 0.04 \)) averts ~8% of peak cases (387 vs. 422), and mindfulness training (standardized mean difference = -0.42, modeled as \( \gamma \to 0.025 \)) averts ~8% of peak cases (387 cases).Conclusions: This framework promotes ethical, evidence-based strategies for burnout prevention across preclinical and residency training phases, with extensible applications to other social epidemics, including depression and anxiety contagion through SEIR model variants.