Predicting the number of visceral leishmaniasis cases in Kashgar, Xinjiang, China using the ARIMA-EGARCH model

Objective: To forecast the visceral leishmaniasis cases using autoregress integrated moving average (ARIMA) and hybrid ARIMA-EGARCH model, which offers a scientific basis to control visceral leishmaniasis spread in Kashgar Prefecture of Xinjiang, China. Methods: The data used in this paper are monthly visceral leishmaniasis cases in the Kashgar Prefecture of Xinjiang from 2004 to 2016. The sample data between 2004 and 2015 were used for the estimation to choose the best model and the sample data in 2016 were used for the forecast. Time series of visceral leishmaniasis started on 1 January 2004 and ended on 31 December 2016, consisting of 1 790 observations reported in Kashgar Prefecture. Results: For Xinjiang, the total number of reported cases were 2 187, the male-to-female ratio of cases was 1:1.42. Patients aged between 0 and 10 years accounted for 82.72% of all reported cases and the largest percentage of visceral leishmaniasis cases was detected among scattered children who accounted for 68.82%. The monthly incidences fitted by ARIMA (2, 1, 2) (1, 1, 1)12 model were consistent with the real data collected from 2004 to 2015. However, the predicted cases failed to comply with the observed case number; we then attempted to establish a hybrid ARIMA-EGARCH model to fit visceral leishmaniasis. Finally, the ARIMA (2, 1, 2) (1, 1, 1)12- EGARCH (1, 1) model showed a good estimation when dealing with volatility clustering in the data series. Conclusions: The combined model has been determined as the best prediction model with the root-mean-square error (RMSE) of 7.23% in the validation phase, which means that this model has high validity and rationality and can be used for short-term prediction of visceral leishmaniasis and could be applied to the prevention and control of the disease.