Application of ARIMA, ARIMAX, and NGO-LSTM models in forecasting the incidence of tuberculosis cases in Liaocheng City, Shandong Province

doi:10.19982/j.issn.1000-6621.20230253

Abstract

Abstract:

Objective: The purpose of this study was to determine the optimal model for predicting tuberculosis incidence in Liaocheng City, Shandong Province by comparing the Autoregressive Integrated Moving Average (ARIMA) model, the Autoregressive Integrated Moving Average with Exogenous Regressors (ARIMAX) model, and the Long Short-Term Memory (LSTM) model combined with the Northern Goshawk Optimization (NGO) algorithm. Methods: Monthly tuberculosis case data from January 2011 to December 2018 were collected. We constructed ARIMA model, ARIMAX model, and NGO-LSTM model based on data from January 2011 to December 2017, respectively, and evaluate the performance of the three models in predicting the number of tuberculosis cases in 2018. Results: The mean absolute percentage errors (MAPE) for the ARIMA model, the multivariate ARIMAX model considering the monthly average relative humidity (lagged by 1 month) and the minimum temperature (lagged by 2 months), and the NGO-LSTM model for predicting tuberculosis incidence in 2018 were 9.293%, 8.419%, and 5.820%, respectively. The mean absolute errors (MAE) were 19.282, 16.997, and 13.119, respectively, and the root mean square errors (RMSE) were 23.773, 22.191, and 16.297, respectively. Conclusion: Among the three models, the NGO-LSTM model had the best predictive performance for monthly tuberculosis incidence in Liaocheng City, providing a new idea for the establishment of a tuberculosis alerting system and scientific basis for relevant departments to make decisions on tuberculosis prevention and control policy.

Key words: Tuberculosis, Time, Models, statistical, Forecasting

CLC Number:

R183.3

Sun Minghao, Duan Yuqi, Zheng Liang, Yu Shengnan, Cheng Chuanlong, Zuo Hui, Chen Ming, Li Xiujun. Application of ARIMA, ARIMAX, and NGO-LSTM models in forecasting the incidence of tuberculosis cases in Liaocheng City, Shandong Province[J]. Chinese Journal of Antituberculosis, 2023, 45(12): 1177-1185. doi: 10.19982/j.issn.1000-6621.20230253

Figures/Tables 13

模型	MAPE(%)	MAE	RMSE
ARIMA(3,1,3)×(0,1,0)₁₂	10.330	21.546	27.637
ARIMA(3,1,3)×(1,1,0)₁₂	9.891	21.213	27.115
ARIMA(3,1,3)×(2,1,0)₁₂	10.734	23.210	29.985
ARIMA(3,1,3)×(0,1,1 $) 12 a$	9.293^a	19.282^a	23.773^a
ARIMA(3,1,3)×(1,1,1)₁₂	10.182	21.458	27.323
ARIMA(3,1,3)×(2,1,1)₁₂	10.477	21.879	27.834
ARIMA(3,1,3)×(0,1,2)₁₂	10.203	21.505	27.369
ARIMA(3,1,3)×(1,1,2)₁₂	9.559	20.209	24.642
ARIMA(3,1,3)×(2,1,2)₁₂	11.067	23.991	31.434
ARIMA(3,1,3)×(1,1,1)₁₂+MAT(lag2)	10.725	22.367	28.948
ARIMA(3,1,3)×(0,1,1)₁₂+MAHT(lag3)	11.385	24.427	31.737
ARIMA(3,1,3)×(1,1,1)₁₂+MALT(lag3)	10.001	21.242	27.27
ARIMA(3,1,3)×(1,1,1)₁₂+MAH(lag1)	9.539	19.409	24.313
ARIMA(3,1,3)×(1,1,1)₁₂+MAP(lag3)	10.971	23.429	30.636
ARIMA(3,1,3)×(1,1,1)₁₂+MAS(lag4)	12.198	24.806	34.857
ARIMA(3,1,3)×(1,1,1)₁₂+MALT(lag3)+MAH(lag1)	8.626	17.825	22.992

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变量	均值	标准差	最小值	下四分位数	中位数	上四分位数	最大值	四分位距
月发病数(例)	244.53	44.45	153.00	212.00	244.00	268.50	432.00	56.50
MAT(℃)	14.34	10.13	-4.10	4.20	15.54	24.40	29.37	20.20
MALT(℃)	9.86	10.07	-8.95	-0.16	10.69	19.79	25.91	19.94
MAHT(℃)	19.92	10.16	1.40	9.66	22.00	29.24	33.67	19.58
MAH(%)	65.31	10.71	41.68	57.02	64.69	74.49	83.97	17.48
MAP(hPa)	1012.39	8.87	997.03	1003.98	1013.04	1020.06	1027.74	16.08
MAS(m/s)	2.05	0.43	1.23	1.76	2.03	2.31	3.34	0.55

ARIMA模型	赤池信息准则	P值 (Ljung-Box检验)
ARIMA(3,1,3)×(0,1,0)₁₂	772.728	0.881
ARIMA(3,1,3)×(1,1,0)₁₂	755.954	0.870
ARIMA(3,1,3)×(2,1,0)₁₂	757.713	0.853
ARIMA(3,1,3)×(0,1,1)₁₂	751.211	0.881
ARIMA(3,1,3)×(1,1,1)₁₂	752.925	0.786
ARIMA(3,1,3)×(2,1,1)₁₂	754.639	0.808
ARIMA(3,1,3)×(0,1,2)₁₂	752.962	0.785
ARIMA(3,1,3)×(1,1,2)₁₂	754.891	0.789
ARIMA(3,1,3)×(2,1,2)₁₂	755.252	0.826

因子	滞后时间
因子	0个月	1个月	2个月	3个月	4个月	5个月	6个月	7个月	8个月	9个月	10个月	11个月	12个月
MAT	-0.070	0.114	0.063	-0.298^a	0.153	-0.181^a	-0.049	-0.036	-0.010	0.096	0.029	0.031	0.063
MAHT	-0.057	0.087	0.042	-0.048	0.260	-0.059	-0.271^a	0.011	-0.071	0.020	0.087	-0.057	-0.024
MALT	-0.030	0.028	-0.215^a	-0.006	0.068	-0.197	-0.050	-0.001	0.068	0.117	-0.011	-0.003	0.074
MAH	0.043	-0.094^a	-0.033	-0.050	-0.013	-0.090	0.044	-0.025	-0.004	0.058	-0.058	0.033	-0.007
MAP	0.019	-0.062	-0.233^a	0.014	-0.058	0.080	0.120	-0.137	-0.041	-0.100	0.007	0.080	-0.023
MAS	0.093	0.030	-0.157	0.073	0.038	0.177^a	-0.049	0.041	0.081	-0.041	0.082	0.015	0.102

模型	拟合			预测
模型	MAPE(%)	MAE	RMSE	MAPE(%)	MAE	RMSE
ARIMA(3,1,3)×(0,1,1)₁₂	8.063	20.190	29.896	9.293	19.282	23.773
ARIMA(3,1,3)×(0,1,1)₁₂+MAT(lag3)	8.026	20.085	29.741	9.345	19.397	23.961
ARIMA(3,1,3)×(0,1,1)₁₂+MAT(lag5)	8.418	21.312	31.056	10.952	22.995	33.213
ARIMA(3,1,3)×(0,1,1)₁₂+MAHT(lag6)	9.187	22.879	33.823	9.496	20.751	24.206
ARIMA(3,1,3)×(0,1,1)₁₂+MALT(lag2)	8.040	20.134	29.794	9.181	19.075	23.493
ARIMA(3,1,3)×(0,1,1)₁₂+MAH(lag1)	7.643	19.210	29.616	8.598	17.788	22.988
ARIMA(3,1,3)×(0,1,1)₁₂+MAP(lag2)	8.330	20.721	30.030	10.830	21.775	32.471
ARIMA(3,1,3)×(0,1,1)₁₂+MAS(lag5)	8.658	21.767	32.016	11.941	24.029	34.291
ARIMA(3,1,3)×(0,1,1)₁₂+MALT(lag2)+MAH(lag1)	7.330	18.983	29.227	8.419	16.997	22.191

参数调整	最大迭代次数	学习率衰减的起始迭代次数	学习率衰减因子	优化器	NGO种群数量	NGO迭代次数	MAPE (%)	MAE	RMSE
原模型^a	2000^a	850^a	0.2^a	Adam^a	10^a	30^a	5.820^a	13.119^a	16.297^a
减小最大迭代次数	1000	850	0.2	Adam	10	30	6.448	13.386	18.600
增大最大迭代次数	3000	850	0.2	Adam	10	30	6.236	12.180	16.903
减小学习率衰减的起始迭代次数	2000	450	0.2	Adam	10	30	6.384	13.260	17.230
增大学习率衰减的起始迭代次数	2000	1250	0.2	Adam	10	30	7.973	16.919	20.479
减小学习率衰减因子	2000	850	0.1	Adam	10	30	5.950	11.649	16.829
增大学习率衰减因子	2000	850	0.3	Adam	10	30	5.887	11.466	16.661
改变优化器	2000	850	0.2	RMSprop	10	30	8.313	17.612	21.324
减小NGO迭代次数	2000	850	0.2	Adam	10	20	5.914	11.242	16.788
减小NGO迭代次数	2000	850	0.2	Adam	10	25	6.719	14.472	19.401
增大NGO迭代次数	2000	850	0.2	Adam	10	35	8.023	17.311	21.115
增大NGO迭代次数	2000	850	0.2	Adam	10	40	7.267	16.665	19.552
减小NGO种群数量	2000	850	0.2	Adam	5	30	7.245	16.173	19.470
增大NGO种群数量	2000	850	0.2	Adam	15	30	6.044	11.813	16.862
增大NGO种群数量	2000	850	0.2	Adam	20	30	6.664	14.049	18.977