Establishment And Analysis Of Tuberculosis Dynamics Model And Time Series Model In Kashgar,Xinjiang

Objective:To explore the application of infectious disease dynamics model,one-dimensional time series ARIMA model and multivariate time series ARIMAX model in the confirmatory research and epidemiological trend prediction of tuberculosis epidemic situation in Kashgar,Xinjiang.According to the results of kinetic verification,a predictive model consistent with the epidemic characteristics of tuberculosis was established for the actual incidence of tuberculosis in Kashgar.Understand the overall epidemic trend of tuberculosis in Kashgar,Xinjiang,and provide a scientific basis for relevant departments to prevent and control tuberculosis in advance.Methods:?1?Using the kinetic model to fit the tuberculosis data of 14 places?states and municipalities?in Xinjiang from 2005 to 2014,and use the 2015-2017 tuberculosis data to verify the results of the verification,and obtain the estimation of the parameters of each region.The value and the basic regeneration number R₀,based on the size of the basic regeneration number of 14 prefectures,quantitatively verified the severity of the tuberculosis epidemic in southern Xinjiang,especially in the Kashgar region.?2?Secondly,the stability of the original sequence was tested against the sequence chart of tuberculosis incidence in Kashgar and the ADF test.The sequence is non-stationary.To eliminate the trend and seasonality of the sequence,a first-order ordinary difference?d=1?and a first-order seasonal difference?D=1?are applied to stabilize it.Next,we examined the autocorrelation plot?ACF?and the partial autocorrelation plot?PACF?to identify the parameters in the model:p,q,P,and Q,respectively.Then,the Maximum Likelihood Estimation?MLE?method is used to estimate the parameters in the model.In order to evaluate the applicability of the established ARIMA model,the parameters and residuals of the model were tested separately,and the Ljung-box?Q?test was used to check whether the residual of the model was white noise.Finally,if several models satisfy the condition that the parameters are significant and the residual sequence of the model is white noise,then Akaike Information Criterion?AIC?,Schwarz Bayesian Information Criterion?SBC?,Model RMSE Indicator and MAPE can be used to select the most.Excellent single variable model.?3?In order to establish an optimal multivariate model,we consider meteorological variables as regression variables in the model to test whether they can improve the predictive performance of ARIMA.Cross-correlation analysis was performed on the number of tuberculosis cases and climate data to find the best predictor and its final lag period and incorporate it into the final model.In order to eliminate the trend and seasonal characteristics of each meteorological variable sequence,each meteorological variable needs to be differentially processed to achieve stability.Next,a pre-whitening process is performed to establish an optimal ARIMA model for each individual meteorological variable,which is used as a filter to filter the input sequence and the output sequence.Finally,the cross-whitening process is completed by calculating the cross-correlation coefficient between the filtered output sequence and the input sequence through a cross-correlation function?CCF?.The hysteresis relationship between the input sequence and the output sequence was judged by the cross-correlation plot,and the multivariate ARIMA model included climate variables significantly associated with the number of tuberculosis cases?P value<0.05?.In summary,the ARIMA model with input variables is called the dynamic regression model,abbreviated ARIMAX.The best selection criteria for the ARIMAX model are still AIC and MAPE.Results:The kinetic model results show that R0 in the Kashgar region of southern Xinjiang is 11.38?95%CI:11.33 to 11.50?.The R0 of Urumqi City in the eastern Xinjiang region and the Ili Kazakh Autonomous Prefecture in the northern Xinjiang region are 5.46?95%CI:5.28 to 5.50?and 2.22?95%CI:2.18 to 2.28?,respectively.The tuberculosis epidemic in southern Xinjiang is much higher than that in northern Xinjiang and eastern Xinjiang,especially in Kashgar.Secondly,the univariate seasonal ARIMA?0,1,1?×?0,1,1?₁₂2 model is the best model for predicting tuberculosis cases in Kashgar,Xinjiang?mean square error in verification phase,MAPE=16.77%?.We incorporate the meteorological data obtained as a regression variable into the univariate model to improve the prediction accuracy of the model.The ARIMAX model was used to analyze the correlation between the number of tuberculosis cases and meteorological factors in the Kashgar region of Xinjiang from 2011to 2017.The monthly precipitation was 7 months lag,the floating dust days were 4months lag,the monthly average temperature was 0 months lag,and the sunshine hours were 6 months lag introduced into the univariate model.The results showed ARIMA?0,1,1??The monthly precipitation model of 0,1,1?₁₂+7 months lag can improve the predictive performance of the univariate model?MAPE=12.53%of the verification phase?.Conclusion:The tuberculosis kinetics model in this paper is well fitted and feasible,and the verification results are reliable.The time series model can be used as a useful tool to predict tuberculosis cases in Kashgar,Xinjiang.Therefore,it can provide a scientific basis for the prevention and treatment of tuberculosis.Introducing meteorological variables into the model can improve its accuracy.