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 [Almutairi et al. 2022], rising to 44.2% before residency [Frajerman et al. 2019] 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 [Almutairi et al. 2022], transmission rate β=0.05 (weekly, derived from longitudinal escalation [Hansell et al. 2019]), recovery rate γ=0.02 (mindfulness effects, SMD=-0.42 [Shi et al. 2021]), and relapse rate δ=0.01. Hierarchical priors are informed by empathy-burnout correlations (ESr=-0.15, 95% CI [-0.21, -0.10] [Bergman et al. 2024]) and stress models (β_stress=0.39 [Kim et al. 2024]). MCMC posteriors (10,000 iterations) yield E[β_stress]=0.40 (95% HDI [0.35, 0.45]), E[β_empathy]=-0.16 (95% HDI [-0.21, -0.11]). Parameter sweep analysis attributes 85% of peak variance to β; 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 [Hansell et al. 2019]). Interventions (e.g., pass/fail grading, OR=1.4 [Perlis et al. 2024]; 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