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TPF are notifiable diseases in China. GMs predict the future values of a time series based only on a set of the most recent data depending on the window size of the predictor. It is assumed that all data used in grey models are positive, and the sampling frequency of the time series is fixed.

In grey systems theory, GM n , m denotes a grey model, where n is the order of the difference equation and m is the number of variables. In grey system theory, a grey prediction model is one of the most important parts, and the GM 1, 1 model is the core of grey prediction. The purpose of GM 1, 1 model is to work on system forecasting with poor, incomplete, or uncertain messages.


The GM 1, 1 model has more advantages over those traditional prediction ways, because it does not need to know whether the prediction variables obey normal distribution, and also does not require too much statistic sample. In order to smooth the randomness, the primitive data obtained from the system to form the GM 1, 1 is subjected to an operator, named Accumulating Generation Operator. The differential equation [ie, GM 1, 1 ] is solved to obtain the n-step ahead predicted value of the system.

Finally, using the predicted value, the Inverse Accumulating Generation Operator is applied to find the predicted values of original data. To some processes, x 1 k is the solution of the following white-formed ordinary differential equation. The equation 1 is called GM 1, 1. The solution of 1 is:. The equation 2 is called time response function. Model with preferable fitting accuracy can be used to extrapolate predicted value.

Otherwise, residual correction has to be carried out first. Usually, posterior error detection method is used to test the accuracy of GM 1, 1. The indexes of fitting testing includes posterior error ration C and small error probability P. Posterior error ration C is the ratio of residual standard deviation S e and data standard deviation S x. Obviously, if the residual standard deviation is smaller, the prediction accuracy is more excellent.

The specific formula is as followed:. If the result of fitting test is satisfactory, the model can be considered as credible. Then predicted value can be extrapolated by the followed formula:.

Excel was used to set up the database and establish predicting model for TPF incidence. Actual reported incidences of TPF from to in Wuhan were taken as time series to build GM 1, 1 predicting model. Its functional equation is as followed:. Goodness of Fit Test showed that prediction accuracy grade C is 0. So the established model can be used in extrapolated prediction.

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Incidences of TPF from to in Wuhan city were fitted and the results showed that estimated values coincided with the actual values. Actual values in was 0. The average of absolute residual value was 0. Comparison of actual value and estimate value of typhoid and paratyphoid fevers incidence.


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Based on the established functional equation, a short-term extrapolated prediction was carried out to estimate incidences of TPF from to Extrapolated prediction showed that the incidences of TPF from to were 0. The incidences of TPF were obviously slowly decreasing. Time series prediction refers to the process by which the future values of a system is forecasted based on the information obtained from the past and current data points.

Statistical and artificial intelligence—based approaches are the 2 main techniques for time series prediction seen in the literature. However, these techniques are not accurate for nonlinear problems. More importantly, they need large number of samples and are too complex to be used in predicting future values. In contrast, grey system theory is a better alternative method for time series prediction, which is designed to work with system in which the available information is insufficient to characterize the system.

For instance, if the information is known entirely, the system is called a white system. If the information is unknown, it is called a black system. If the information is being incomplete, it can be named as a grey system. Strictly, every system can be considered as a grey system because there are always some uncertainties. Because of the noise from both inside and outside of the system, the information we can reach about that system is always uncertain and limited in scope. As superiority to conventional statistical approaches, grey system theory requires only a limited number of data to estimate the behavior of unknown systems, which is different from the previous methods.

Because of its simple calculation process and higher forecasting accuracy, grey system theory has been widely used in the prediction of a lot of fields. In recent years, grey system theory has become more and more popular in biomedical information and technology. In grey system theory, GM 1, 1 model is an effective approach, which can make use of relatively small data sets and does not require to comply with certain statistical laws strictly, simple or linear relationships among the observable variables. Thus, it can overcome the disadvantages of statistical method.

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In the present study, based on the raw data of TPF incidence from to in Wuhan City, GM 1, 1 model was built to forecast the incidence in the next 3 years. The model accuracy examination results show that GM 1, 1 model is able to make accurate predictions for forecasting incidence of TPF. We compared actual value with predicted value in The result showed that predicted values are consistent with actual values, indicating that GM 1, 1 model we built is credible and effective in practice. Traditional TPF incidences estimation methods use statistics analysis, so that large data samples are required.

With restricted conditions, it usually causes the results lack of authenticity and unsuitable to apply in practical use. By using the grey system modeling, the more reliable prediction can be obtained for future policy making in TPF prevention. In addition, incidences of infectious diseases are deeply influenced by social and natural factors, so database of grey model should be updated in time for long-term analysis. Contaminated water and food are important vehicles for transmission of TPF and preventive public health measures based on sanitation and hygiene have proved to be essential to the reduction of TPF.

Therefore, careful food preparation and washing of hands are crucial in preventing TPF. Adequate water treatment, waste disposal, and protection of the food supply from contamination are also important public health measures. In addition, carriers of TPF must not be allowed to work as food handlers.

And finally, the use of TPF vaccines will be helpful to reduce the susceptibility of hosts to infection. It was reported that the incidence of TPF was high among the residents of the densely populated urban community. The incidence of TPF demonstrates the need for longer-term investment in improvement of water and sanitation services to reduce the burden of multiple fecal-oral transmitted pathogens in these communities.

Targeted vaccination against TPF would be a valuable immediate step to reduce disease burden, especially in densely populated urban community. However, more emphasis should be placed upon sanitary improvements and health education, rather than focusing solely on improving the health delivery system.

It is also likely that an important proportion of cases are due to travels.

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Pretravel screening and vaccination strategies are essential measures for travelers to endemic areas. Our present study must be interpreted in light of some limitations. Secondly, we have not construct train set, because the data are actually not big enough for training a GM model if being divided into train set, validation set, and test set.

Therefore, expanding the data of TPF should be considered for future research. In conclusion, the purpose of the present study was to adopt grey system theory to predict the incidence trend of TPF in Wuhan City, and provide reference for the government in policy making. Our study shows that grey forecasting model GM 1, 1 we built is an effective forecast method and can be used to predict the incidence of TPF. This finding may serve as a reference to future studies and policy making.

Conceived and designed the experiments: GFJ.

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Analyzed the data: JJZ. Wrote the article: XBY. XY and JZ contributed equally to this work. The authors of this work have nothing to disclose. National Center for Biotechnology Information , U.