A Theoretical Framework for Hybrid Deterministic SIRS Modeling and Bayesian Hierarchical Inference in Burnout Propagation in Medical Education: Calibrated Simulations, Risk Factor Analysis, and Intervention Projections

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.背景：全球范围内约37%至56%的医学本科生受职业倦怠（burnout）困扰，在住院医师培训前这一比例攀升至约44%，对医疗人力队伍的可持续性构成严重威胁。 方法：本理论手稿提出一种混合建模框架，整合了用于描述职业倦怠传播的确定性易感-感染-恢复-易感（Susceptible-Infected-Recovered-Susceptible, SIRS）模型，以及结合元分析先验信息的贝叶斯层级推断风险因素分析方法。经校准的关键参数包括：初始患病率0.3723；每周传播率0.05（源自纵向增长模式推导）；恢复率0.02（对应正念干预效果，标准化均数差=-0.42）；复发率0.01。层级先验纳入了共情-职业倦怠相关性（效应量r=-0.15）与压力相关系数（0.39）。基于10000次迭代的马尔可夫链蒙特卡洛（Markov chain Monte Carlo, MCMC）后验分布得以估算。通过参数扫描与蒙特卡洛模拟开展敏感性分析，其中参数取自正态分布：$ eta sim mathcal{N}(0.05, 0.005) $，$ gamma sim mathcal{N}(0.02, 0.002) $，$ delta sim mathcal{N}(0.01, 0.001) $。 结果：敏感性分析显示，压力水平与传播率的变化对职业倦怠峰值患病率具有显著影响，后验分布估算得到压力系数为0.40（95%最高密度区间：0.35--0.45），共情系数为-0.16（95%最高密度区间：-0.21-- -0.11）。参数扫描结果表明，峰值患病率方差的85%可由传播率解释；而蒙特卡洛模拟显示，针对1000人的队列，其95%预测区间为380至485例。后验预测检验（p=0.07）验证了模型与观测到的经验峰值（三年级学生中占比45%）的拟合度。预计的干预措施，如及格/不及格评分制（优势比=1.4，建模为$ eta o 0.04 $）可避免约8%的峰值病例（387例对比422例），而正念训练（标准化均数差=-0.42，建模为$ gamma o 0.025 $）同样可避免约8%的峰值病例（387例）。 结论：本框架可为临床前与住院医师培训阶段的职业倦怠预防提供符合伦理且基于证据的策略，其可扩展应用于其他社会传播流行病，包括通过易感-暴露-感染-恢复（Susceptible-Exposed-Infected-Recovered, SEIR）模型变体实现的抑郁与焦虑传播。