A Theoretical Bayesian SIR Modeling Framework for Burnout Propagation in Medical Education: Calibrated Simulations, Hierarchical Inference, and Intervention Projections

Burnout affects 37.23% (95% CI: 32.66--42.05%) of medical undergraduates globally \cite{almutairi2022prevalence}, rising to 44.2% before residency \cite{frajerman2019burnout} and threatening workforce sustainability. This theoretical manuscript presents a falsifiable framework that integrates an extended Susceptible-Infected-Recovered (SIR) model for burnout contagion with Bayesian hierarchical inference based on meta-analytic priors. Calibrated parameters include initial prevalence \( I(0)/N=0.3723 \) \cite{almutairi2022prevalence}, transmission rate \( \beta=0.05 \) (weekly, derived from longitudinal escalation \cite{hansell2019temporal}), recovery rate \( \gamma=0.02 \) (mindfulness effects, SMD=-0.42 \cite{shi2021mindfulness}), and relapse rate \( \delta=0.01 \). Hierarchical priors are informed by empathy-burnout correlations (ESr=-0.15, 95% CI [-0.21, -0.10] \cite{bergman2024empathy}) and stress models (\( \beta_{\text{stress}}=0.39 \) \cite{kim2024predictive}). MCMC posteriors (10,000 iterations) yield \( \mathbb{E}[\beta_{\text{stress}}]=0.40 \) (95% HDI [0.35, 0.45]), \( \mathbb{E}[\beta_{\text{empathy}}]=-0.16 \) (95% HDI [-0.21, -0.11]). Parameter sweep analysis attributes 85% of peak variance to \( \beta \); Monte Carlo propagation provides 95% prediction intervals [380, 460] cases (\( N=1000 \)). Posterior predictive checks (\( p=0.07>0.05 \)) confirm fit to empirical peaks (45% in year 3 \cite{hansell2019temporal}). Interventions (e.g., pass/fail grading, OR=1.4 \cite{perlis2024interventions}; mindfulness, 22% peak reduction) are projected to mitigate 15--30% of incidence. Reproducible Python/PyMC code enables verification. This framework supports ethical, evidence-based prevention of burnout across preclinical to residency phases, with broader implications for social epidemics, including depression and anxiety contagion via SEIR extensions.Keywords: Burnout, Medical Education, SIR Model, Bayesian Inference, Sensitivity Analysis, Social Epidemics, SEIR Model