Application and comparison of time-varying SEIQDR and ARIMA models in COVID-19 prediction in Shanghai
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摘要:
目的 根据时变易感者-潜伏者-感染者-隔离者-死亡者-康复者(susceptible-exposed-infected-quarantined-dead-removed, SEIQDR)模型和差分自回归移动平均(autoregressive integrated moving average, ARIMA)模型，针对上海市Omicron感染数据选择适合上海市疫情判断的预测模型。 方法 选用2022年3月1日—4月20日上海市COVID-19新增阳性感染者的数据进行拟合，选用2022年4月21日—5月30日的数据评估模型的预测效果。分别构建时变SEIQDR模型与ARIMA模型，通过比较决定系数(coefficient of determination, R2)、平均绝对误差(mean absolute error, MAE)和均方根误差(root mean squared error, RMSE)的大小评价模型的拟合及预测效果。 结果 时变SEIQDR模型和ARIMA模型的拟合效果均较优，R2分别为0.990和0.984。2个模型5 d的预测效果均尚可，对于20 d以及40 d预测效果，时变SEIQDR模型更优且更符合传染病传播的规律；前者的40 d预测MAE和RMSE分别为1 001.461和1 967.704，后者分别为1 265.331和2 068.094，且时变SEIQDR模型能较好地实现对上海市本轮疫情变化趋势及发病人数的复现。 结论 时变SEIQDR模型可较好地拟合及预测上海市COVID-19的发病人数及变化趋势，且模型效果优于ARIMA(2, 2, 0)。 -
关键词:
- 新型冠状病毒感染 /
- 时变易感者-潜伏者-感染者-隔离者-死亡者-康复者模型 /
- 时间序列 /
- 差分自回归移动平均模型
Abstract:Objective Based on the time-varying susceptible-exposed-infected-quarantined-dead-removed (SEIQDR) model and autoregressive integrated moving average (ARIMA) model, the Omicron infection data in Shanghai were studied and judged. The two models′ fitting, prediction effect and applicability were analyzed and compared. And the prediction model with a better effect and suitable for developing the epidemic in Shanghai, China was selected. Methods Data from March 1, 2022 to April 20, 2022, for newly infected cases in Shanghai were selected for fitting. Data from April 21, 2022 to May 30, 2022, were used to evaluate the prediction effect of the model. Time-varying SEIQDR models and ARIMA models were constructed, respectively. The models′ fitting and prediction effects were evaluated by comparing the magnitudes of R2, MAE, and RMSE. Results Both the time-varying SEIQDR model and the ARIMA model had a better fitting effect, with R2 of 0.990 and 0.984, respectively. The 5-day predictions of both models were fair, and the time-varying SEIQDR model was better and more consistent with the pattern of infectious disease transmission for the 20-day and 40-day predictions, with the 40-day predicted MAE and RMSE of 1 001.461 and 1 967.704, respectively, for the former and 1 265.331 and 2 068.094, respectively, for the latter. The time-varying SEIQDR model was able to achieve a more complete replication of the trend of the current epidemic and the number of incidences in Shanghai. Conclusions The time-varying SEIQDR model can better fit and predict the number and trend of COVID-19 in Shanghai, and the model effect is better than that of ARIMA(2, 2, 0). -
图 1 时变SEIQDR传播动力学模型示意图
SEIQDR：易感者-潜伏者-感染者-隔离者-死亡者-康复者。
Figure 1. Schematic diagram of time-varying SEIQDR transmission dynamics model
SEIQDR: susceptible-exposed-infected-quarantined-dead-removed.
图 2 ARIMA模型流程图
ARIMA：差分自回归移动平均。
Figure 2. Flow chart of ARIMA model
ARIMA: autoregressive integrated moving average.
图 3 时变SEIQDR模型拟合及预测图
SEIQDR：易感者-潜伏者-感染者-隔离者-死亡者-康复者。
Figure 3. Fitting and prediction diagram of time-varying SEIQDR model
SEIQDR: susceptible-exposed-infected-quarantined-dead-removed.
图 5 原始序列ACF和PACF图
ACF：自相关；PACF：偏自相关。
Figure 5. ACF and PACF diagrams of the original sequence
ACF: autocorrelation function; PACF: partial autocorrelation function.
图 7 二阶差分序列ACF和PACF图
ACF：自相关；PACF：偏自相关。
Figure 7. ACF and PACF diagrams based on the second-order difference
ACF: autocorrelation function; PACF: partial autocorrelation function.
图 8 ARIMA模型残差Q-Q图
ARIMA：差分自回归移动平均。
Figure 8. Residual Q-Q plot of ARIMA model
ARIMA: autoregressive integrated moving average.
图 9 ARIMA(2, 2, 0)模型与时变SEIQDR模型的拟合与预测对比
ARIMA：差分自回归移动平均；SEIQDR：易感者-潜伏者-感染者-隔离者-死亡者-康复者。
Figure 9. Fitting and prediction comparison between the ARIMA (2, 2, 0) model and time-varying SEIQDR model
ARIMA: autoregressive integrated moving average; SEIQDR: susceptible-exposed-infected-quarantined-dead-removed.
表 1 时变SEIQDR模型参数赋值
Table 1. Parameter assignment of time-varying SEIQDR model
参数 Parameters 描述 Interpretations 取值 Value 来源 Source β0 有效接触率 Effective contact rate 0.088 MCMC c 接触数 Number of contacts 20.000 实际疫情 Actual epidemic w 指数下降率(t≥t1) Index decline rate (t≥t1) 0.016 MCMC θ 潜伏者相对于感染者的传染率系数 Infectivity coefficient of exposed 0.997 MCMC q 隔离率 Quarantine rate 0.100 实际疫情 Actual epidemic σ 潜伏期倒数 Incubation rate 0.333 实际疫情 Actual epidemic δI 阳性感染者向住院患者的转化速率 Hospitalization rate of infected 0.801 MCMC δq 隔离潜伏者向住院患者的转化速率 Hospitalization rate of quarantined exposed 0.799 MCMC α 因病死亡率 Disease related mortality rate 0.002 实际疫情 Actual epidemic λ 隔离解除速率 Quarantine release rate 0.071 实际疫情 Actual epidemic γI 阳性感染者康复率 Recovery rate of infected 0.103 MCMC γH 住院患者康复率 Recovery rate of hospitalized 0.101 MCMC v 免疫阈值(疫苗接种率×疫苗保护率) Immunity threshold (vaccination rate×vaccine protection rate) 0.720 实际疫情 Actual epidemic h 抗体滴度水平下降率 Reduction rate of the antibody level 0.500 实际疫情 Actual epidemic 注：SEIQDR, 易感者-潜伏者-感染者-隔离者-死亡者-康复者; MCMC, 马尔科夫链蒙特卡洛。
Note: SEIQDR, susceptible-exposed-infected-quarantined-dead-removed; MCMC, Markov Chain Monte Carlo.
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表 2 ARIMA模型参数估计和模型检验
Table 2. Parameter estimation and model testing of ARIMA model
指标 Indicator ARIMA(0, 2, 3) ARIMA(2, 2, 0) 估计值
Estimated valuet值
valueP值
value估计值
Estimated valuet值
valueP值
value参数估计 Parameter estimation AR(1) — — — -0.605 -5.410 ＜0.001 AR(2) — — — -0.636 -5.675 ＜0.001 MA(1) 0.631 4.418 ＜0.001 — — — MA(2) 0.191 1.137 0.262 — — — MA(3) -0.331 -2.314 0.025 — — — 拟合优度 Goodness of fit AIC 856.170 849.350 BIC 14.856 14.649 Box-Ljung χ2 0.307 1.158 P值 value 0.580 0.282 注：1. AR，自回归；MA，移动平均；AIC，赤池信息准则；BIC，贝叶斯信息准则。
2. “—”表示该模型不存在此阶参数。
Note: 1. AR, autoregressive; MA, moving average; AIC, Akaike information criterion; BIC, Bayesian information criterion.
2. "—" the model does not have this order parameter.
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表 3 模型评价指标对比
Table 3. Comparison of model evaluation indexs
模型 Model 拟合R2
Fitted R2预测天数
Predicted number of days预测效果 Predicted effects MAE RMSE 时变SEIQDR Time-varying SEIQDR model 0.990 5 d 5 195.653 5 637.511 20 d 1 741.019 2 604.237 40 d 1 001.461 1 967.704 ARIMA(2, 2, 0) 0.984 5 d 4 286.145 4 757.543 20 d 1 850.111 2 851.169 40 d 1 265.331 2 068.094 注：SEIQDR，易感者-潜伏者-感染者-隔离者-死亡者-康复者；ARIMA，差分自回归移动平均；R2，决定系数；MAE，平均绝对误差；RMSE，均方根误差。
Note：SEIQDR，susceptible-exposed-infected-quarantined-dead-removed；ARIMA，autoregressive integrated moving average；R2，coefficient of determination；MAE，mean absolute error; RMSE，root mean squared error.
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