基于马尔可夫链和隐马尔可夫模型的庆阳市乙型肝炎发病趋势预测

Prediction of incidence trend of hepatitis B base on Markov chain and hidden Markov model in Qingyang

目的为准确地预测乙型肝炎发病趋势,根据乙型肝炎发病的变化特点,提出基于马尔可夫链(Markov chain,MC)和隐马尔科夫模型(hidden Markov model,HMM)的传染病预测模型以预测乙型肝炎的发病趋势。方法对2015年1月—2016年10月甘肃省庆阳市分月乙型肝炎发病数分组后,通过交叉验证MC将其划分为5个状态,利用时间与状态的转移概率矩阵进行MC预测;对2015年1月—2016年10月庆阳市分月乙型肝炎发病数差分,假定HMM的隐状态为3后,通过状态转移概率和发射概率矩阵进行HMM预测;选择2016年11月和12月乙型肝炎发病数作为验证集,分别对MC和HMM的预测效果进行验证。结果 MC预测2016年11月和12月发病数分别为91和94,平均绝对误差(mean absolute error,MAE)为17,均方误差(mean squared error,MSE)为298;HMM预测发病数2016年11月和12月分别为77和69,MAE为8.5,MSE为78.5。结论建立的MC和HMM能够捕捉乙型肝炎发病变化规律,无需了解影响被预测变量的相关因素,即可进行预测;HMM和MC相比,HMM有较好的预测精度。

Objective To propose a prediction model base on Markov chain（MC） and hidden Markov model（HMM） according to the epidemic characteristics of hepatitis B to predict the incidence trend. Methods After grouping the monthly case number of hepatitis B in Qingyang from January 2015 to October 2016, five states were divided by cross-validation of MC. The MC prediction was made by using the matrix of transition probability of time and state. HMM prediction was made through state transition probability and matrix of emission probability after difference calculation of monthly incidence of hepatitis B in Qingyang from January 2015 to October 2016 and assumed the hidden state as three. The incidence of hepatitis B in November and December 2016 was used as the verification set to verify the predictive effect of MC and HMM respectively. Results The incidence of hepatitis B predicted by MC was 91 in November and 94 and in December 2016, respectively, with mean absolute error（MAE） of 17 and mean squared error（MSE） of 298. The result predicted by HMM in November and December 2016 was 77 and 69 respectively with MAE of 8.5 and MSE of 78.5. Conclusions The prediction models based on MC and HMM can catch the epidemic regulation of hepatitis B without understanding the influence factors.HMM is of better prediction accuracy than MC.