Time-series Analysis For Measles In Hebei Province

Objective:By the intensive and rough control measures, the eliminate measles goal that the measles incidence can be drop to less than 1/1000,000 in 2012 has been reached in Hebei province. But the achievement was not keeped, the incidence has increased 10 times in the next year, and the increase was more fierce in 2014. On the basis of the existed working experence in Hebei Province, this paper is going to establish the quantitative forecast model and warning mechanism with quantitative indicators for measles epidemic, with coordinating and guiding the current work methods, to provide evidence for developing more fine and effective strategies and measures to truly achieve the goal of eliminating measles.Method:To build the ARIMA model for the yearly measles incidence from 1979 to 2013, the quarterly, monthly and weekly measles cases from 2001.1 to 2014.9 by EViews8.0. The building model process mainly includes the model identification; model parameter estimation and model inspection; forecasting. To establish the four layers time series model that is including yearly, quarterly, monthly and weekly measles epidemic for Hebei Province, in order to adapt to different job purpose and meet the different needs of the work. To use the the 95% CL forecasting values as measles epidemic early warning line, and to assess the historical data, alert the current and impending epidemic by the warning line.Results:1 The measles epidemic feathure in Hebei provinceThe measles incidence was on the wavy falling trend since 1950 in Hebei province, but the incidence was considerably high and fluctuated before 1979, then it showed a relatively low level and stable after 1979. There was a peak and valley in the annual measles incidence, this single peak mainly appeared in the period from March to June, the highest point was in April or May, and mainly in May. Even from 2011 to 2013, these lower incidence level years, the measles epidemic has still appeared obvious periodic feathure.2 Establishing the yearly ARIMA model and using it to forecast and warnSet up the time series yt by the annual measles incidence, after have been tested as a stationary series, the identificated model was ARIMA(1,0,0). Through parameter, model and residual test, the finally selected model was ARIMA(1,0,0) without constant, and the equation was(1-0.73B)yt=et. These evaluation indexes of forecasting: the Theil Inequality Coefficient was 0.33, BP=0.04, VP=0.07, and CVP=0.89, these result indicated that the selected model was fitting and forecasting well. The fitted value curve basicly tallied with the actual value curve. Out of the sample, the forecasting incidence was 0.04/100,000 in 2013, the actual incidence was 0.54/100,000 that fell into the 95% CL(9.76/100,000) of forecasting value. The forecasting incidence was 0.39/100,000 in 2014, and the warning line was 10.11/100,000, compared with early onset, the forecasting showed a rising trend, so it was need to alert.3 Establishing the quarterly ARIMA model and using it to forecast and warnSet up the time series qt by the quarterly measles cases, forecasting from the SARIMA(0,0,1)(0,1,3)4 model that directly fitted from series qt, the fitted value curve didn’t tally with the actual value curve. After natural log transformated on the series qt, the new identificated model was SARIMA(0,1,2)(0,1,3)4 without constant, and the equation was ▽▽4ln(qt)=(1-0.31B2)(1+1.26B4-0.32B12)et. The Theil Inequality Coefficient of the pre-model was 0.42, the new was 0.21 that decreased half of the before. The pre-model’s BP ≈ 0, VP=0.07 and CVP=0.93, but the new model’s BP=0.01, VP=0.03 and CVP=0.96, this is to say that the new model has been improved the fitting and forecasting better than the before one. Compared with the pre-model, the new model’s fitting value was more tallied with the actual value curve, and there were no negative forecasting value appeared. Out of the sample, the forecasting cases were 249 in the third quarter of 2014, the actual cases were 182 that fell into the 95% CL(897 cases) of forecasting value. The forecasting cases were 97 in the fourth quarter of 2014, and the warning line was 326 cases, compared with early onset, the forecasting showed a downward trend that was basically tallied with the periodic trend of past years.4 Establishing the monthly ARIMA model and using it to forecast and warnSet up the time series mt by the monthly measles cases, after natural log transformated the series qt to ln(mt+1), then differenced to stationary, the identificated model was SARIMA(3,1,2)(2,1,2)12. Through parameter, model and residual test, the finally selected model was SARIMA(2,1,2)(1,1,2)12 without constant, and the equation was(1-0.73B2)(1+0.73B12) ▽▽12ln(mt+1)=(1+0.75B2)(1+0.85B24)et. The Theil Inequality Coefficient was 0.13, BP ≈ 0, VP=0.05, CVP=0.95, these result indicated that the selected model was fitting and forecasting well. Out of the sample, the forecasting cases were 63 in September of 2014, the actual cases were 18 that fell into the 95% CL(155 cases) of forecasting value. The forecasting cases were 18 in October of 2014, and the warning line was 45 cases, compared with early onset, the forecasting showed a downward trend that was basically tallied with the periodic trend of past years.5 Establishing the weekly ARIMA model and using it to forecast and warnSet up the time series wt by the weekly measles cases, after natural log transformated the series qt to ln(wt+1), then differenced to stationary, the identificated model was SARIMA(1,1,1)(2,1,2)52. Through parameter, model and residual test, the finally selected model was SARIMA(1,1,1)(2,1,2)52 without constant, and the equation was(1+0.24B)(1+0.83B52)(1+0.17B104) ▽▽52ln(wt+1) =(1+0.33B)(1+0.87B104)et. The Theil Inequality Coefficient was 0.11, BP ≈ 0, VP=0.01, CVP=0.99, these result indicated that the selected model was fitting and forecasting well. Out of the sample, the forecasting cases were 6 in the 38 th week of 2014, the actual cases were 6 that fell into the 95% CL(14 cases) of forecasting value. The forecasting cases were 5 in the 39 th week of 2014, and the warning line was 16 cases, compared with early onset, the forecasting showed a downward trend.Conclusion:1 The combined use of four layers time series model for measles epidemic that can be used to enhance the forecasting accuracy and extend the prediction time period, and make up for the deficiency of single model.2 Coordinating with the normal assessment methods, the measles series model can be used to instantly evaluate the current strategies and measures and warning the future epidemic, for to guide the work of the next step.3 Working with the infectious disease report, to establish the three time layers forecasting and warning mechanism for measles epidemic by using the quarterly, monthly and weekly series model. Step by step, these three layer models can work together to defend measles epidemic.