Forecasting incidence of hemorrhagic fever with renal syndrome in China using ARIMA model

Hemorrhagic fever with renal syndrome (HFRS), or epidemic hemorrhagic fever (EHF) is an acute viral syndrome caused by infection with one of hantaviruses. HFRS is an important infectious disease in developing countries. In China, HFRS is caused mainly by 2 types of hantaviruses, Hantaan virus (HTNV) and Seoul virus (SEOV), each of which has coevolved with a distinct rodent host. HTNV is associated with Apodemus agrarius, whereas SEOV, which causes a less severe form of HFRS, is associated with Rattus norvegicus [1]. In hantavirus -endemic areas, HFRS is most common among farmers and others who may have close contact with excreta of infected rodents [2, 3]. In mainland China, HFRS remains a serious public health problem with approximately 20,000-50,000 human cases reported annually, approximately 90% of the total cases worldwide [4‐6]. Currently, HFRS is endemic in 28 of 31 provinces in mainland China [4, 7].

In response to the spread of HFRS in China, the Chinese Center for Disease Control and Prevention designed a surveillance system for HFRS and created educational programs for the general public. However, the impact of control efforts remains difficult to measure due to the inherent complexities of HFRS as a disease: multiple viral strains with identified genetic polymorphisms, complex disease manifestation, diverse animal reservoirs, and multiple routes of transmission [8]. Infectious diseases have certain characteristic features that lead themselves to modeling, such as: speed of pathogen variation, accumulation of susceptible hosts, and environmental indices [9]. Thus, epidemic modeling and forecasting can be essential tools to prevent and control HFRS. Recently, statistical methods including linear regression [10‐12], correlation coefficients [13], grey swing model [14], back propagation artificial neural network model [15] have been used for prediction of HFRS incidence. The variation of HFRS incidence, which is influenced and constrained by diversified factors, is characterized by tendency and randomicity. These statistical tools are inappropriate for analyzing the randomicity of HFRS. Autoregressive integrated moving average (ARIMA) models, which take into account changing trends, periodic changes, and random disturbances in time series, are very useful in modeling the temporal dependence structure of a time series. In epidemiology, ARIMA models have been successfully applied to predict the incidence of infectious diseases, such as influenza mortality [16], malaria incidence [17], as well as other infectious diseases [18, 19]. This study aimed to develop a univariate time series model for the HFRS incidence; specifically, a stochastic ARIMA model, for short-term forecasting of HFRS incidence (per 100,000 population) in China.

Time series analysis of surveillance data on incidence of various infections is very helpful in developing hypotheses to explain and anticipate the dynamics of the observed phenomena and subsequently in the establishment of a quality control system and reallocation of resources [22]. ARIMA model is one of the most widely used time-series forecasting techniques because of its structured modeling basis and acceptable forecasting performance [23]. In this paper, we applied an ARIMA(p, d, q) model to analyze the surveillance data of HFRS in China. Disease monitoring by public health department entails ongoing data collecting, processing, and updating. However, the national level China CDC is the appropriate level of organization for the implementation of an ARIMA predictive model, because reported data is continually received and updated. We found that model predictions are further improved by the assured availability of the Health Department data. In this study, we have obtained an ARIMA model that closely fits HFRS incidence in China. The autoregression and moving average parameters of our model imply the incidence of HFRS in a month can be estimated by the residual occurring one month prior. According to the results above, the conducted model is reliable with a high validity. Once a satisfactory model has been obtained, it can be used to forecast expected numbers of cases for a given number of future time intervals [24]. Thus, the fitted ARIMA(0,3,1) model can be used to predict the next three years' HFRS incidence in China. The forecast results suggest that the HFRS incidence in China will experience a slight growth in the next three years (2009-2011). A rise in the number of HFRS incidence may also result from an increase in the number and size of natural foci [25], climate change, especially the increase of mean temperature [26, 27]. Therefore, knowledge of HFRS forecasts is necessary to prompt health departments to strengthen surveillance systems and reallocate resources in anticipation of increasing HFRS incidence.

Several studies have used ARIMA model to fit and predict changing trends in infectious disease. Luz et al applied an ARIMA(2,0,0)×(1,0,0)₁₂ model to predict dengue incidence in Rio de Janeiro [18] and found that ARIMA models were useful tools for monitoring dengue incidence. Earnest et al indicated that ARIMA models provided useful tools for administrators and clinicians in planning for real-time bed capacity during infectious diseases outbreaks such as SARS [28]. Li et al have applied an ARIMA model to monthly incidence of HFRS in Linyi City, China to predict HFRS incidence, and found that the ARIMA model could be used to predict HFRS incidence with high predictive precision in the short-term [29]. In the present study, we further confirmed the consensus that ARIMA model is a useful tool in monitoring and predicting changing trends in infectious diseases.

To the best of our knowledge, this is the first study to apply ARIMA model to fit the HFRS incidence in China with as many as 34 observations at year level. Some previous studies [30, 31] in China also used ARIMA model to fit and forecast HFRS incidence of some regions, but they had the same problem that the number of observations was not enough, which led to the instability of their forecast results. In order to conduct a stable and effective ARIMA model, we have to collect at least 30 observations [32]. Thus, parameter estimates of the fitted model would be more robust. The longer the series, the better; however, the series should not extend so far into the past as to include periods during which a different case definition was applied or in which any other reporting artifact resulted in a mean number of cases per interval that differs from the mean of recent intervals. As mentioned above, for adequate ARIMA modeling, a time series should be stationary with respect to mean and variance. If the mean increases or decreases over time, or if the variance does, the series may need to be transformed to make it stationary, before being modeled. Otherwise, the prediction effect of the model will be poor.

In order to improve the model, updating the forecasts is very important. A model without seasonal terms will need to be updated frequently. Confidence intervals that widen rapidly as time increase from the starting point of the forecasts also indicate a model that needs frequent updating. Generally speaking, there are two ways to implement the updating. The model can be reapplied to the original series with extra observations added at the end to give forecasts based on a later starting point. Alternatively, a new model can be fitted to the longer series. This is probably preferable, since fitting a model is quick, especially when the old model is used as a guide, and it makes better use of the additional observations.

Some limitations of this study also need to be taken into account when interpreting the results. In this study, the interval of HFRS incidence is one year, so we could not analyze its seasonal characteristic. In further study, we would use monthly data to predict HFRS incidence in order to get seasonal pattern and higher predictive precision. In addition, the data are from a passive surveillance system, the possible biases in disease reporting and potential underreporting of HFRS cases might influence the precision of our analysis.

There is an urgent need for monitoring and predicting HFRS incidence to reduce the substantial morbidity and mortality caused by this disease [33]. ARIMA models applied to historical HFRS incidence data are an important tool for HFRS surveillance. Accurate forecasting of the incidence of HFRS is possible. Our modeling approach can be used to monitor and predict HFRS incidence in China. The ARIMA model could be used to optimize HFRS prevention by providing estimates on HFRS incidence trends in China.