Epidemic Peaks Forecasting on Re-emerging Diseases in Elderly People using the Grey Disaster Model

Climate change causes the spread of non-vector diseases due to the influence of climate uncertainty. The elderly group, which is vulnerable, is affected by such disasters. Therefore, the objectives of this study were to forecast epidemic peaks of food poisoning, which was found as one of the re-emerging diseases in elderly people in Khon Kaen Province, Maha Sarakham Province, and Roi Et Province, which are in the Northeastern region of Thailand by using 2 types of Grey Model: GM(1,1) and Discrete Grey Model (DGM). The monthly rate of food poisoning incidence per 100,000 elderly people from January 2017 to December 2020 i.e., 48 months in total were used in the study. The study result revealed that the DGM had higher forecasting effectiveness than that of the GM(1,1) in all three provinces. The food poisoning incidences in elderly people were forecasted to re-emerge from August to September 2021 in Khon Kaen Province, from August to September 2022 in Maha Sarakham Province, and from May to June 2022 in Roi Et Province. The results of this study are useful and helpful for the government, the Ministry of Public Health and related cooperatives to effectively help services planning resource preparation and prevention measures.

Page | 975 are widely used in medicines [4][5][6][7][8][9], and other areas such as petroleum, geological engineering, industry, management, marketing, and agriculture [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In medicines and public health, the spread of diseases is affected by several uncertain factors, so the Grey theory with dynamic changes is suitable to be used. The GM(1,1) is popularly used in forecasting diseases and death rates from epidemics. As a result, this research studied the epidemic peaks of food poisoning of elderly people in Khon Kaen Province, Maha Sarakham Province, and Roi Et Province (Thailand) since those provinces were almost in the top ranks of elderly people with food poisoning in the middle northeastern region. The analyses with GM(1,1) and DGM are useful for planning resources and preventing the diseases effectively.

2-1-Data
The data in this research were the monthly rate of food poisoning incidence per 100,000 elderly people from January 2017 -December 2020 i.e., 48 months in total in Khon Kaen Province, Maha Sarakham Province, and Roi Et Province.

2-2-GM(1,1)
GM(1,1) is the model of the Grey theory of prediction with one variable .The first order Grey model is created with a few data (four or more ) . Its procedure is as follows:  The existing data with the sample units are represented in (0) , ..., ( )),  Calculate the cumulative sum of the existing data (0) X in the form of a cumulative sum series.
 Calculate (1) Z , the means from (1) as:  Calculate for the differential equation of GM(1,1) with The resulting derivative of a function is (0) a and b are the parameters of GM(1,1).
And the new equation is adjusted as follows: It is called the time response equation.
The least square method is used to estimate the parameters in the equation: then the recursive function is used with the following setting:   (9) where 1, 2,..., 1 kn  .

2-4-Model Accuracy Test
The model accuracy tests are as follows;  Mean Relative Error where     For determining 0 0 C  , if the variance ratio is is calculated for probability of small errors and for determining 0 > 0 ;where > 0 , the forecasting model is regarded as satisfied.
The used scale for testing the model accuracy is illustrated in Table 1.  Figure 1 shows the procedure for processing this research.  Table 2 shows the monthly rate of food poisoning incidence per 100,000 elderly people from January 2017-December 2020 in Khon Kaen Province, Maha Sarakham Province, and Roi Et Province. The data at 4 epidemic peaks were selected for the analyses with GM(1,1) and DGM as shown in Figures 2 to 4.      Table 3 .The values of forecasting and relative errors of GM(1,1) and DGM in each province are shown in Table 4, whereas the results from the model accuracy testing of GM(1,1 ) and DGM in each province are shown in Table 5.   In this study, the incidence rate of food poisoning of elderly people was conducted in Khon Kaen Province, Maha Sarakham Province and Roi Et Province which are located in the Northeastern region of Thailand. It was found that the 4 epidemic peaks of food poisoning incidence rate of elderly people in Maha Sarakham Province and Roi Et Province occurred from July to September, which is during the rainy season. In Khon Kaen Province, 4 epidemic peaks of food poisoning incidence rate of elderly people occurred in April 2018, January 2019, September 2019, and July 2020. It is shown that the first epidemic peak occurred during the summer season and tends to occur during the rainy season. The rainy season of Thailand is tropical and the pathogens may be growing as well. If people are not careful when eating, it may result in gastrointestinal diseases such as food poisoning, especially in the elderly people with low immunity, it can lead to death. In this research, the GM(1,1) model and the DGM model were used to construct the grey disaster model. The simulation results showed that the DGM model had a better performance. Then, the DGM model was chosen to make the prediction, which is corresponding to Shen et al. [5].

4-Conclusion
Grey disaster prediction, the GM(1,1) and DGM, is important to predict the time of abnormal values, and propose the forecast of the exact times of forthcoming disasters to prepare ahead of time for the worst situation. In this study, the GM(1,1) and DGM were used for forecasting the epidemic peaks of food poisoning incidence in the elderly people in Khon Kaen Province, Maha Sarakham Province, and Roi Et Province in Thailand .The study found that the DGM had higher forecasting effectiveness than that of the GM(1,1) in all three provinces .When the DGM is used in forecasting, the forecasting value in Khon Kaen Province was found at ̂( 0) (5) = 56.40223, meaning that food poisoning incidence would re-emerge in elderly people from August to September 2021 and the mean relative error of the DGM model is 0.298% . In Maha Sarakham Province, the forecasting value was found at ̂( 0) (5) = 68.83143, meaning that food poisoning incidence would re-emerge in elderly people from August to September 2022 and the mean relative error of the DGM model is 0.029%. In addition, the forecasting value in Roi Et Province was found at ̂( 0) (5) = 65.03383, meaning that food poisoning incidence would re-emerge in elderly people from May to June 2022 and the mean relative error of the DGM model is 0.021%. Although the forecasting with Grey theory is highly effective and has yielded good results, it may not be appropriate for all situations. Moreover, the forecasting with Grey theory is more accurate in the short term but its accuracy in long-term forecasting may decrease [24]. Therefore, we should consider and analyze the actual situation and select a suitable model and adapt it to the situation of the disease. This makes it possible to take full advantage of forecasting models to maximize long-term benefits.

5-2-Data Availability Statement
The data presented in this study are available on request from the corresponding author.

5-3-Funding
This research project was financially supported by Thailand Science Research and Innovation Fund (TSRI) 2021 and Mahasarakham University.

5-4-Acknowledgements
This research project was financially supported by Thailand Science Research and Innovation Fund (TSRI) 2021 and Mahasarakham University. The authors would like to thank the associate editor and the referees.

5-5-Conflicts of Interest
The authors declare that there is no conflict of interests regarding the publication of this manuscript. In addition, the ethical issues, including plagiarism, informed consent, misconduct, data fabrication and/or falsification, double publication and/or submission, and redundancies have been completely observed by the authors.