Introduction
Japanese encephalitis is considered as a secondary legal infectious disease in Korea and is one of the main mosquito-borne infectious diseases of the summer season.
Culex tritaeniorhynchus, which transmits Japanese encephalitis, is dispersed not only in Korea, but also in other areas such as Japan, China, Southeast Asia, India, and Pakistan. This major mosquito species infects approximately 68,000 individuals each year, resulting in approximately 20,000 deaths annually
[1–3].
Since the first reported incidence of the disease in Korea from the U.S. forces stationed in the Incheon area in 1946
[4,5], the incidence of Japanese encephalitis has significantly increased since 1949, affecting at least 5616 people, and resulting in 2797 deaths
[6,7]. Moreover, 1000–3000 individuals were infected with the disease each year until the 1960s. The incidence of Japanese encephalitis significantly decreased in the 1970s compared with the 1960s. From 1984 to 2009, this infectious disease was almost eradicated, with less than 10 cases reported every year. However, 28 cases were reported in 2010, with a possibility of an increase in vector mosquito density due to changes in temperature and the environment. Thus, continuous prevalence prediction is warranted.
Seasonal identification is very important in managing mosquitoes
[8]. It has been reported that the rapid decrease in the incidence of Japanese encephalitis between 1960 and 1970 was due to the decrease in the density of the vector mosquito
[9–11], which is similar to that observed in Japan
[12,13].
In this research, black light traps were installed in 10 regions of Korea (Busan, Gyeonggi, Gangwon, Chungbuk, Chungnam, Jeonbuk, Jeonnam, Gyeongbuk, Gyeongnam, and Jeju) for the last 12 years from 1999 to 2012 and mosquito data were collected. Using the data collected, a simple AR(p) model was used to estimate and predict the ratio of Japanese encephalitis vector mosquitoes. Thus, this research was conducted to predict mosquito occurrence in order to control the incidence of Japanese encephalitis.
Materials and methods
2.1 Data
Data for this investigation were directly acquired by the National Institutes of Health from the Public Health and Environment Research Institute of 10 regions in Korea (Busan, Gyeonggi, Gangwon, Chungbuk, Chungnam, Jeonbuk, Jeonnam, Gyeongbuk, Gyeongnam, and Jeju), two times a week from May to October (data collection period: 1999–2012). In addition, this investigation used the mosquito occurrence density data of Japanese encephalitis prediction programs of the last 14 years using the mosquito classification key of the regional health centers.
2.2 Collection region and equipment
Cowsheds have been identified as the main region of vector mosquito occurrence in all the 10 Korean regions. A black light trap, which is commonly used for mosquito density studies, was installed at a height of 1.5–1.8 m within the cowshed. The light traps were operated two times a week from 19:00
pm to 06:00
am the following day
[14]. The mosquitoes collected in the trap were carefully transported to the laboratory. Then, the mosquitoes were placed in a plastic bag with a cotton ball of ether or chloroform. Next, the plastic bag was completely sealed or kept in the freezer for at least 2 hours. After killing, the mosquitoes were identified and classified by observing them under a dissection microscope. Based on the number of mosquitoes collected, the daily average density of mosquitoes was calculated (i.e., mosquitoes/trap/night).
2.3 Preliminary data analysis
Figure 1 shows the distribution of
Cx. tritaeniorhynchus and all other mosquitoes in Korea by week from 1999 to 2012. The population of all mosquitoes including
Cx. tritaeniorhynchus changed at 2–3-year intervals. Moreover, after 2010, the
Cx. tritaeniorhynchus population decreased compared with the population of all other species of mosquitoes. These changes might have been caused by an increase in its natural enemies or temperature, although this analysis did not include the analysis of factors affecting mosquito density and mainly focused on predicting the population dynamics of mosquitoes.
2.3.1
2.3.1 Unit root test
The time series using the unit root test is relatively unstable. Therefore, this may cause problems of spurious regression, especially when using general regression analysis. Thus, the variables and mosquito data used in this study were executed using a unit root test to verify whether these could be considered as stable time-series data. The augmented Dickey–Fuller test
[15] and Phillips–Perron test
[16] were used for the unit root test.
Table 1 shows the results of the unit root test using the mosquitoes collected/week. In the table, “none” indicates the absence of a constant term and trend; “intercept” indicates a constant term; and both constant term and trend are considered as “trend.” The null hypothesis that the unit root exists in the rates of all mosquitoes and
Cx. tritaeniorhynchus was rejected and the unstable-level variables were used in the analysis.
2.3.2
2.3.2 Summary statistics
Table 2 shows the results of the statistical analysis. The ratio of all mosquitoes to
Cx. tritaeniorhynchus was positive (+). The density of all mosquitoes was highest in 2003 (87,194 mosquitoes). The density of
Cx. tritaeniorhynchus was highest in 2007 (58,769 mosquitoes), which was the highest value ever recorded.
2.3.3
2.3.3 Lag selection
Before the prediction using the AR(
p) model, the Akaike information criterion and the Schwarz information criterion tests were used to determine the proper time deviation
p.
Table 3 shows the density of all mosquitoes 1 week before the analysis, as well as the
Cx. tritaeniorhynchus density and ratio variable 4 weeks before the analysis. The autocorrelation function was used to validate the time difference, which was high in the 1-year unit (
Figure 2) and was maintained for 4 years. Thus, the data from the same period of last year to the same period 4 years ago were used to predict the AR figure.
2.4 Methods
The AR(
p) model used in this research is presented in Eq.
(1). Each
p predicts the same period of last year's AR(
p) model.
AR(
p) model was used to execute the in-sample and out-of-sample analyses. For the in-sample prediction,
β, which is the estimation gained from the prediction of the total period, was used for the in-sample estimation, as shown in Eq.
(2).
For the out-of-sample prediction, two methods were used, namely, rolling regression (RO) and adding regression (AD). First, the RO is a prediction method while moving a certain number of samples. In cases of insufficient data, it is not advisable to use the prediction method. Second, the AD method executes the out-of-sample prediction by accumulating the samples. The out-of-sample prediction in this study initially predicts mosquito density until 2007. Then, the sample was moved by 1-year units for prediction analysis. The
t data were used for the out-of-sample prediction analysis and the
y˜t+1 of
t + 1 is the same as Eq.
(3).
After executing an in-sample estimation and an out-of-sample prediction, the mean-square prediction errors (MSPEs) were calculated to select the model that shows superior prediction results. MSPE pertains to the average of the square of the difference between the actual value and the estimation. A smaller MSPE value indicates a relatively superior prediction.
Results
Table 4 shows the prediction results of the AR model using the same period of last year. Similar to most cases, the AR model generates a significant value.
Mean square error (MSE) was calculated to compare the estimation of the model according to the variable using the predicted results.
Table 5 shows the MSE value when predicting the in-sample model described in
Table 4.
Table 6 shows the MSPE calculated during the out-of-sample prediction of the model as shown in
Table 4. Two methods can be used for the out-of-sample prediction as described earlier. First, the RO is a method for prediction while moving the interval number of the sample. When data are insufficient, an inaccurate prediction might be generated. Second, the AD method executes the out-of-sample prediction by accumulating the sample. The out-of-sample prediction here initially predicts up to 2007. The sample was then moved by 1-year units for prediction. In this research, two cases were analyzed. However,
Table 6 shows that the MSPE generated using the AD method was smaller when the sample size was smaller than the population of mosquitoes.
Figure 3 shows the out-of-sample results used in the RO analysis. For 2013–2016, past estimations were used to identify the predicted values. First, the ratio of all mosquitoes and
Cx. tritaeniorhynchus gradually increased from 2013 with regular changes. For
Cx. tritaeniorhynchus, the term of the change was shorter compared with all mosquitoes. However, using the RO method, the accuracy of the value that barely appeared in
Cx. tritaeniorhynchus in 2013 was lower compared with that using the AD method.
Figure 4 shows the results of the out-of-sample prediction using the AD method. The difference in the estimation and the actual value between 2009 and 2012 was low compared with that shown in
Figure 3. In addition, when looking at the estimations from 2013 to 2016, 2013 showed a decrease in the density of
Cx. tritaeniorhynchus, and an increase was detected a year later. By contrast, the ratio of all mosquitoes to
Cx. tritaeniorhynchus gradually decreased.
Discussion
In this research, the data on mosquito density for the Japanese encephalitis prediction program acquired from the Public Health and Environment Research Institute of 10 regions in Korea from May to October of 1999 to 2012 were used in the AR(p) model. The MSPEs of the in-sample and out-of-sample predictions were compared. The relatively superior model was used to predict the future mosquito populations.
The MSPE value was low when the AR method was used. When prediction was executed using the AR method, the mosquito population again showed an increase and a decrease in a certain term and interval. For the estimations of 2013–2016 using estimations of up to 2012, the density of Cx. tritaeniorhynchus initially decreased in 2013, and then increased. By contrast, the ratio of all mosquitoes to Cx. tritaeniorhynchus showed a gradual decrease.
Not only Cx. tritaeniorhynchus but all mosquitoes are influenced by factors related to their habitat such as number of disinfection events, temperature, and rainfall as related to humidity. If these factors are appropriately controlled, more superior results could be acquired for the prediction of Cx. tritaeniorhynchus and all other mosquitoes. However, when predicting with methodologies such as the Kalman filter to control these factors, this methodology could also be confusing. In addition, there is a possibility that the result will not be exact due to the lack of data or other factors that cannot be observed. Thus, based on the properties of the data on Cx. tritaeniorhynchus and all mosquitoes, the ratios of all mosquitoes to Cx. tritaeniorhynchus were predicted through a relatively simple AR(p) model. Furthermore, the Cx. tritaeniorhynchus population initially decreased and subsequently increased, although the density of Cx. tritaeniorhynchus decreased compared with that of all mosquitoes.
