Time Prediction Models for Echinococcosis Based on Gray System Theory and Epidemic Dynamics

Echinococcosis, which can seriously harm human health and animal husbandry production, has become an endemic in the Xinjiang Uygur Autonomous Region of China. In order to explore an effective human Echinococcosis forecasting model in Xinjiang, three grey models, namely, the traditional grey GM(1,1) model, the Grey-Periodic Extensional Combinatorial Model (PECGM(1,1)), and the Modified Grey Model using Fourier Series (FGM(1,1)), in addition to a multiplicative seasonal ARIMA(1,0,1)(1,1,0)4 model, are applied in this study for short-term predictions. The accuracy of the different grey models is also investigated. The simulation results show that the FGM(1,1) model has a higher performance ability, not only for model fitting, but also for forecasting. Furthermore, considering the stability and the modeling precision in the long run, a dynamic epidemic prediction model based on the transmission mechanism of Echinococcosis is also established for long-term predictions. Results demonstrate that the dynamic epidemic prediction model is capable of identifying the future tendency. The number of human Echinococcosis cases will increase steadily over the next 25 years, reaching a peak of about 1250 cases, before eventually witnessing a slow decline, until it finally ends.