基于贝叶斯方法与季节性动力学模型的中国肺结核发病数预测与防控措施评估

Prediction of the pulmonary tuberculosis incidence and control measures assessment in China based on Bayesian method and seasonal dynamic model

目的考虑肺结核发病的季节周期性,构建动力学模型,拟合并预测中国肺结核月发病数,为相关部门优化防控措施提供参考依据。方法首先,基于季节性分解(seasonal-trend decomposition using loess,STL)模型和易感者-接种者-早期潜伏者-晚期潜伏者-感染者-治疗者(susceptible-vaccinated-early latent-late latent-infected-treated,SVELIT)模型,建立STL-SVELIT动力学模型。然后,利用2017―2021年的中国肺结核月发病数拟合模型,通过贝叶斯框架对参数进行估计,并计算模型的基本再生数(basic reproduction number,R0)。最后,预测中国肺结核发病的流行趋势。在措施评估方面,基于R0的敏感性分析来模拟肺结核的防控措施。具体来说,通过降低疾病传播系数β、早期和晚期潜伏人群向活动性肺结核患者的进展速率θ1和θ2以及出现症状的比例p3,评价不同肺结核防控措施效果。结果基于2017―2021年肺结核月发病数、利用STL-SVELIT模型STL-SVELIT模型拟合的平均绝对百分比误差(meanabsolute percentage error,MAPE)=4.30%,预测2022年1月―2023年5月肺结核月发病数时MAPE=6.57%,具有良好的拟合效果和预测精度。估计R0=2.076,表明肺结核在中国仍然流行。模拟结果显示,参数β降低75.00%时,预测2035年中国肺结核发病率为29.1/10万;参数θ1、θ2同时降低75.00%时,预测2035年中国肺结核发病率为25.4/10万;参数β、θ1、θ2和p3同时降低75.00%时,预测2035年中国肺结核发病率为11.1/10万。结论降低疾病传播系数和潜伏期进展速率对控制肺结核疫情有效,但需要综合多种措施才能实现世界卫生组织提出到2035年的控制目标(发病率低于10.0/10万)。

Objective Considering the seasonal periodicity of pulmonary tuberculosis(PTB),a dynamic model is constructed to fit and predict the monthly PTB cases in China,providing a reference for relevant departments to optimize PTB prevention and control measures.Methods First,based on seasonal-trend decomposition using loess(STL)model and susceptible-vaccinated-early latent-late latent-infected-treated(SVELIT)model,a dynamic model(STL-SVELIT)was established.Then,the monthly PTB cases in China from 2017 to 2021 was used to fit the model.The parameters of the model and further the basic reproduction number(R0)were estimated in the Bayesian framework,in order to predict the epidemic trend of PTB in China.In terms of intervention evaluation,sensitivity analysis based on R0was conducted to simulate the prevention measures for PTB.Specifically,the effects of various PTB prevention and control measures were evaluated by reducing the value of parameters:β,which represents the disease transmission coefficient;θ1,θ2,which accounts for the progression rate from latent individuals to active PTB patients in both early and late stages;and p3,which indicates the proportion of symptomatic cases.Results The Mean Absolute Percentage Error(MAPE)was 4.30%when using the monthly PTB cases from 2017 to 2021 to fit the STL-SVELIT model.MAPE was 6.57%when predicting the monthly PTB cases from January 2022 to May 2023,which has a good fitting effect and prediction accuracy.The model estimated that the R0 of PTB in China was 2.076,suggesting that PTB remains prevalent in the population.Simulation results showed that the predicted PTB incidence in China will reach 29.1 per 100000 in 2035 ifβdeclined by 75.00%;25.4 per 100000 in 2035 ifθ1 andθ2 both decreased by 75.00%;11.1 per 100000 in 2035 if parametersβ,θ1,θ2 and p3all declined by 75.00%.Conclusions Reducing the disease transmission coefficient and the rate of progression of the latent period is effective in controlling the PTB epidemic.However,comprehensive measures are required to achieve the WHO End TB Strategies target in 2035(tuberculosis incidence below 10.0 per 100000).