Infectious Disease Prediction And Control Models Study Based On Grey System Theory

Objective: To investigate the law and prevalence trends of infectious diseases. Based on time-series features and gray system theory, choose the appropriate predictive and control model of infectious diseases. First, according to the dynamic trend of time sequence and grey system theory, an appropriate prediction and control model is established for notifiable infectious diseases in Xinjiang. Secondly, based on the nonlinear feature of time series, a nonlinear grey forecasting model and its optimized models based on modern optimization algorithm to optimize the model parameters are constructed for predicting the incidence of hepatitis B(HB) in Xinjiang. Finally, considering the trend, seasonal, periodic and stochastic volatility in characteristics of the time series, three hybrid grey prediction models are proposed for echinococcosis prediction in Xinjiang and the control strategy are also drew theoretically. Methods: 1) By selecting different dimensions, static grey prediction model and the same dimension dynamic rolling grey model(RGM) are established based on data of notifiable infectious diseases from 2004 to 2010 in Xinjiang. To further verify the model precision, a tuberculosis prediction model based on RGM is established. Three improved grey models, Bayesian based grey prediction model(BGM), least squares based gray prediction model(LSEGM), unbiased grey prediction model(UGM) are also established for comparison with the proposed model. 2) The monthly data set of HB from 2011 to 2012 is collected to constructed genetic algorithm(GA) optimized nonlinear grey Bernoulli prediction model(ONGBM(1,1)), where the 18 observations from January 2011 to June 2012 are used for model building, and the remaining observations from July 2012 to December 2012 are considered to evaluate the out of sample forecasting performance of the model. To test the model precision, traditional GM(1,1), grey Verhulst model(GVM), nonlinear grey Bernoulli prediction model(NGBM(1,1)) are established for compression with the proposed model. 3) Five HB prediction models, the original GM(1,1) model, the GVM model, the Holt-Winters exponential smoothing method, the original NGBM(1,1) model and the optimized Nash nonlinear grey Bernoulli model based on particle swarm optimization(PSO-NNGBM(1,1)) are established for comparison, where incidence data of HB in Xinjiang from January 2012 to August 2012 are regarded as the verifying periods, and September 2012 to December 2012 are reserved for ex post testing. In order to further demonstrate the feasibility and effectiveness of the optimized model in nonlinear prediction, we apply the PSO-NNGBM model to analyze the annual incidence of HB from 2009 to 2012 in Xinjiang, which is a random fluctuation sequence. 4) The 33 observations of echinococcosis from the first quarter of 2004(2004(Q1)) to the first quarter of 2012(2012(Q1)) are used to establish the fitting models and the remaining observations from the second quarter(2012(Q2)) to the fourth quarter(2012(Q4)) are utilized as test object to compare their performance. Based on the underlying data characteristics and the transmission mechanisms of echinococcosis, two hybrid grey models, grey-periodic extensional combinatorial model(PECGM(1,1)) and error modified grey model using Fourier series(FGM(1,1)) are proposed for short-term echinococcosis prediction. Furthermore, a precise grey-dynamic model of echinococcosis transmission is established to evaluate the trend of human echinococcosis incidence and control strategy is also put forward in theory. Results: 1) On the basis of the notifiable infectious diseases data from 2006 to 2010(5 dimensions), the static GM(1,1) with the average relative error =Δ%6.6, grey absolute correlation degree R=980.0, the mean square error ratio C=38.0 and small error probability P=1 has the highest accuracy, and the model precision degree reaches 2. The 6-dimensional static GM(1,1)(2005-2010) with degree 3 has lower precision. The 7-dimensional static GM(1,1)(2004-2010) with degree 4 has the lowest precision, which is not suitable for extrapolation and prediction. The precision degree of RGM(1,1) by using the equivalent dimensions additional one time on the 5-dimensional GM(1,1) can reach to 1, and the precision degree of RGM(1,1) by using the equivalent dimensions additional twice on the 6-dimensional GM(1,1) can also reach to 1. The results of RGM indicate that, by taking effective preventive and treatment measures, the incidence of notifiable infectious diseases in Xinjiang will decline steadily year by year over the next five years. The annual incidence rate can be reduced to no more than 400 per 100,000 people by 2015. 2) The 4 tuberculosis prediction models, 7-dimensional GM(1,1), 6-dimensional GM(1,1), 7-dimensional RGM(1,1) and 6-dimensional RGM(1,1) with precision degree 1, 2, 1 and 1 respectively, have higher precision. The four models are suitable for long-term prediction. The precision of 5-dimensional GM(1,1) model is not satisfactory(degree 3) which is just suitable for short-term prediction. The three models, LSEGM(1,1), BGM(1,1), UGM(1,1)(with degree 3, 4 and 3 respectively) have lower precision than RGM(1,1), which are not suitable for long-term prediction. The fitting results of 7-dimensional RGM(1,1) show that the incidence rate of tuberculosis in Xinjiang will be no more than 128 per 100,000 people by 2020. The overall incidence rate will be falling in 10 years. The short-term prediction results demonstrate that, the incidence rate of tuberculosis in Xinjiang could reach to 151 per 100,000 people in 2015, which is 8 people higher than that of 2004. 3) Fitting results of the 4 HB prediction models(GM(1,1), GVM, NGBM(1,1), ONGBM(1,1)) demonstrate that, the ONGBM(1,1) model with the MAPE=7.43% and the RMSE=1.71 has the highest prediction accuracy than the GM(1,1)(MAPE=8.18% and RMSE=1.75), GVM(MAPE=32.22% and RMSE=7.41), NGBM(1,1)(MAPE=7.87% and RMSE=1.87). Extrapolation results show that, the ONGBM(1,1) with the MAPE=8.79% and the RMSE=1.84 is superior to the (MAPE=8.8952%,RMSE=12.4442) and prediction(MAPE=11.0688%, RMSE=42.0548) when compared to GM(1,1) model and PECGM(1,1) model. The grey models fitting results show that, using present control methods, the echinococcosis will be increasing in short time. 6) Dynamic epidemic prediction model demonstrates the number of human echinococcosis cases will increase steadily in 25 years in the current health conditions and control measures, then reach the theoretical peak(about 1250) and began a slow decline. The basic reproduction ratio 541.00R= indicates that, with the current control measures, human echinococcosis will vanish in Xinjiang in the long run. Conclusion:1)It can be seen that the data of notifiable infectious diseases in Xinjiang is highly non-stationary, non-linear and stochastic. The parameters are revised and prediction values are generated in the dynamic at each step of RGM. The RGM can better reveal the development trend of the system and achieve good prediction effect in mid-long term forecast. 2) The optimized nonlinear grey Bernoulli model based on modern optimization algorithm for parameter optimization is appropriate for incidence time series of HB prediction, which contains trend, random and non-linear in characteristics. 3) When the volatility system is affected by many factors,error correction based prediction models PECGM(1,1) and FGM(1,1) have accuracy higher than that of GM(1,1) prediction model. It’s appropriate to apply PECGM(1,1) and FGM(1,1) for predicting the incidence data of echinococcosis with strong trend, randomicity, seasonality and periodicity. 4) The grey-dynamics model can better grasp the short-term and long-term trend of time series. It is feasible by using the dynamics model to predict the overall trend of echinococcosis in Xinjiang. Numerical simulation results show that by controlling the population size of the definitive host(dog), treating hydatid cysts infected visceral in a strict processing, hunting wild dogs, sick dogs and useless dogs, strengthening the immune of dogs, reducing the infection rate and the number of new dog, regular deworming and controlling the population size of dogs can better control the transmission of echinococcosis. With the strengthening of control measures and the improvement of medical and health conditions, the peak will be, theoretically constantly over backwards.