Application of multiple seasonal ARIMA model in forecasting incidence of HFMD in Wuhan, China

Background: During the last decades, outbreaks of hand-foot-mouth disease (HFMD) have been reported for many times in China. The prevention and control of it has become an issue. Presently, there are no specific treatments and specific antiviral drugs or vaccines available against non-polio enteroviruses causing HFMD. That means the risk of infection only can be reduced by good hygiene practices and early medical attention for children with severe symptoms. Therefore, early detection and response using mathematical statistics method during the epidemics will be helpful for policy-makers to generate preventive strategies. Methods & Materials: We proposed a multiple seasonal auto-regressive integrated moving average model, to forecast the expected incidence from April 2013 to September 2013 using the retrospective incidence from January 2008 to December 2012 as training set, and incidence from January 2013 to March 2013 as validation set obtained from China Information System for Disease Control and Prevention (CISDCP). All the procedures were implemented via SAS9.2 system. Results: After one order of regular differencing and one order of seasonal differencing, the transformed series achieved stationary. The best fitted model was SARIMA with the lowest value of Bayesian Information Criterions (BIC). Model parameters had significant differences (P < 0.05) (Table 1) and the series of residuals considered to be white noise (=14.59, P > 0.05) (Table 2). This indicated that the best fitted model extracted the useful information of the series. Predictions and observations were very close to each other and showed a good forecasting performance. Conclusion: The ARIMA model we proposed can be an effective way to forecast the incidence cases of HFMD. Detecting the outbreaks before they happened is the key point of the early detection and early warning, and that is also the main purpose of our study. The usefulness of forecasting expected incidence of HFMD performs not only in giving public-health officials a probable trend of the variability to be expected in the future, but also in detecting outbreaks and providing probability statements and guidance to policy makers.