Prediction of syphilis incident rate and number in China based on the GM (1,1)grey model

Run-Hua Li ,Jing Huang＊ ,Shun-Ying Luo ,Mei-Ying Zhang

1The Cancer Hospital of the University of Chinese Academy of Sciences (Zhejiang Cancer Hospital),Institute of Basic Medicine and Cancer (IBMC),Chinese Academy of Sciences,Hangzhou,Zhejiang 310022,China.

Abstract Objective:To explore the feasibility of using grey model GM (1,1) model to predict syphilis,and to provide a theoretical basis for the health sector to develop corresponding strategies.Methods:GM (1,1) model was used to construct and simulate the incident rate and case number of syphilis in China from 2009 to 2018 to predict the change trend.Results:The GM (1,1) prediction model of syphilis incident rate was (1) (k+1)=929.367901 e (0.029413k) -906.297901.The GM (1,1) prediction model for the number of syphilis patients was (1) (k+1)=1060.278025 e(0.034280k) -1029.639925.For syphilis incidence model,the posterior difference ratio was0.19819 and the probability of small errorwas1.For the syphilis incident number model,the posterior difference ratio was0.18450 and the probability of small error was 1. The above models have good fitting accuracy with excellent grade level and can be predicted by extrapolation and predicted that the syphilis incidence in 2019-2021 may be 36.15 per 100,000,37.23 per 100,000 and 38.34 per 100,000,respectively.From 2019 to 2021,the number of incident syphilis cases in China may be 503,406,520,962 and 539,130,respectively.Conclusion:The GM (1,1) model can well fit and predict the change trend of syphilis incidence in time series.The prediction model showed that the incidence of syphilis may continue to increase and the number of syphilis cases per year may continue to increase substantially.More effort is needed to strengthen the prevention and treatment of venereal disease,reduce venereal harm to the population and improve the early detection rate of syphilis.

Keywords:Syphilis,Grey model,Prediction

Background

Syphilis are the third most common infectious diseases in China,which cause a great social and economic burden to the population.Therefore,it is of great significance to study the prevalence trend of these diseases [1].Despite the availability of effective treatments,syphilis remains a major public health problem in both developed and developing countries,and the rise in syphilis infection rates coincides with the increase in other sexually transmitted diseases,including HIV infection [2,3].Syphilis is a sexually transmitted disease caused by treponema pallidum,which is very harmful and can affect almost all tissues and organs of the human body.In serious cases,it is life-threatening.Syphilis during pregnancy can also infect the fetus through the placenta,leading to spontaneous abortion,stillbirth or congenital syphilis.The rapid epidemic of syphilis has greatly harmed the health of the broad masses of the people.Syphilis is mainly transmitted through sexual contact.Sexually active people aged 20-39 years old are high incidence groups,and also need to focus on prevention and control of the population.

The epidemic mastering of syphilis incidence prediction is of great significance to the prevention and control of the disease and health decision-making.In our study,by adopting the statistical data of 2009-2018 for syphilis infection situation from China national statistical bureau,we used the grey model GM (1,1)for syphilis incidence equation fitting and accuracy test and the next three years forecast incidence of extrapolation to provide scientific basis for making corresponding health policy for the government health department so as to slow down the syphilis epidemic.

Materials and methods

Data Sources

The incident rate and incident number of syphilis in China from 2009 to 2018 were obtained by collecting and inquiring from the Statistical Yearbook of China.

Methods

The basic principle of gray prediction model is to accumulate the original data to generate the sequence with certain regularity,and then build the corresponding differential equation model to predict the dynamic development process of the system.The steps are as follows [4].

The original data column was χ(0)={χ(0)(t),t=1,2,…,n }

(1) F irst-order ac cumulation t o ge nerate data sequenceχ(1)

The α and u as were the undetermined coefficients.With Z(t) as the independent variable and χ(0)(t) as the dependent variable,the linear regression equation is fitted.The regression coefficient of the equation is α,and the intercept is u [5].

(4) Prediction model

The solution of the above first-order linear differential equation is the estimated value of the accumulated data.

By decreasing and reducing the sequence obtained from the above equation,the estimated value of the original sequence χ(0)(t) can be obtained.

(5) Test the fitting accuracy of the prediction model

The model can only be used for extrapolation prediction if the fitting accuracy is high.The fitting accuracy test indexes of GM (1,1) of the gray prediction model mainly include the posterior difference ratioCand the small error probabilityP,and their calculation formulas are as follows:

C=Se/Sχ，P=P(|e(t)＜0.6745Sx,Where Se is the standard deviation of the fitting error,Se is the standard deviation of the measured values in each year.According to the posterior difference ratioCand small error probabilityP,the fitting accuracy standard of comprehensive evaluation model is shown in Table 1.

All the above calculations were computed by SAS 9.4 statistical software

Table 1 The fitting accuracy grade of GM (1,1) model prediction

Results

Syphilis incident rate and cases in China from 2009 to 2018

The data showed that the incidence of syphilis and the number of cases in China from 2009 to 2018 showed an increasing trend year by year while the incident cases increased to half a million from about 0.3 million(shown in Table 2).

GM (1,1) model of the syphilis incident rate and case

The GM (1,1) model was established by employing the syphilis incidence data from 2009 to 2018.For the prediction model of the syphilis incident rate,the undetermined coefficient α=-0.029413,μ=26.656541,thus the GM (1,1) model of the prediction model of syphilis incidence is(1)(k+1)=929.367901 e(0.029413k)-906.297901,in the residual test,the average relative error △=1.86460%.

In the prediction model of the syphilis incident case,the undetermined coefficient α=-0.034280,μ=35.296289 and the grey GM (1,1) model was(1)(k+1)=1060.278025e(0.034280k)-1029.639925.In the residue test,the mean relative error △=1.95845% (see Table 3).

Test of fitting Effect

For the grey model of syphilis incidence,the posterior difference ratioC=0.19819,the probability of small errorP=1,and the prediction accuracy was excellent grade level.For the grey model of the number of syphilis incidence,the posterior difference ratioC=0.18450 and the probability of small errorP=1 were calculated,and the prediction accuracy was also excellent grade level (see Table 4).Therefore,prediction models of syphilis incident rate and cases can be extrapolated for prediction.

Table 2 Syphilis incident rate and cases in China from 2009 to 2018 (1/100,000)

Table 3 GM (1,1) model test of syphilis incidence and incident number in China from 2009 to 2018

Prediction for 2019-2021 of syphilis

Through the model test fitting effect,the incidence of syphilis model was fitted for precision,and can be further to predict using GM (1,1) model.The model predicted that the national syphilis incidence from 2019 to 2021 would be 36.15/100,000,37.23/100,000 and 38.34/100,000,respectively.From 2019 to 2021,the number of incident syphilis cases in China may be 503,406,520,962 and 539,130,respectively (showed in Table 4).

Table 4 The predicted incident rate and number forecast 2019-2023 in China

Discussion

The scientific prediction of the epidemic disease is the prerequisite for the formulation of short-term or long-term strategies to prevent and control infectious diseases.The grey system theory was established by Chinese scholar Professor Deng Julong in the 1980s[6].It is a prediction tool that is easy to be popularized and applied because it has no strict requirements on sample size and probability distribution [6].GM (1,1)model is the most widely used prediction model among the gray models.It is simple to calculate,has strong applicability and good prediction effect.The occurrence and development of infectious diseases are affected by many factors,such as the quality of infectious disease report in medical institutions,the implementation of prevention and control measures for the prediction of disease species,patients' medical treatment,disease outbreak and epidemic,natural disasters,etc.,which further affect the prediction accuracy of infectious diseases.Therefore,this model is suitable for short-term prediction of diseases with stable epidemic factors.The grey GM (1,1) model has been widely used in agriculture,economy,society,ecology and other fields,especially for the uncertain system of some small samples and poor information[7-9].

The development coefficient α in the GM (1,1)model determines whether the model can be applied to the prediction of disease.When α ≤ 0.3,the GM (1,1)model can be used for medium and long term predictions.When 0.3 ＜ α ≤ 0.5,the GM (1,1) model can be applied to short-term prediction [10] In this study,α1=-0.029413 and α2=-0.034280 met the above conditions for medium and long term predictions.Therefore,it is appropriate to use the grey GM (1,1) model to predict the incidence of syphilis.In this model test,the average relative error of the prediction model of syphilis was 1.86% and 1.96%,respectively.The two GM (1,1) models of the average relative error is within 5%,and the posterior differential ratio is less than 0.35,small error probability was 1,and the prediction accuracy level was the first optimal level,which shows that the GM(1,1) model can be better for syphilis incidence extrapolation prediction.In this paper,the incidence of syphilis among the national statutory infectious diseases is predicted with high accuracy and can be extrapolated. The incidence of syphilis in 2019-2021 may be 36.15 per 100,000,37.23 per 100,000 and 38.34 per 100,000,respectively. From 2019 to 2023,the number of syphilis cases in China may be 503,406,520,962 and 539,130 respectively.

It is significant to understand and grasp the prevalence and development trend of syphilis in time for the prevention of diseases.According to the results of the model,the incidence of syphilis in China from 2009 to 2021 increased year by year,and the number of cases was in the stage of rapid growth,indicating that the epidemic situation of syphilis was severe,the prevention and treatment of syphilis was still very difficult,and sufficient attention should be paid.And current work of syphilis prevention and control should not be limited to report and treatment of patients,and needs to combine behavioral intervention and medical intervention strategies such as extensive propaganda and health education to improve STD prevention and control knowledge,reducing sex partners and promoting the use of condoms with the specification of syphilis treatment services at the same time,strengthening the active detection after engaging with unprotected sex behaviors [11].Medical intervention measures includes improving syphilis screening and case detection rate,enhancing standardized diagnosis and treatment of venereal diseases,promoting sexual partners to test,and timely curing infected sexual partners to reduce the new occurrence of syphilis and other venereal diseases [12].Since syphilis will increase the risk of HIV infection,it is necessary to combine the prevention and treatment of syphilis and AIDS organically,to build a platform for the prevention and treatment of AIDS and syphilis,to simultaneously consult and test,evaluate and screen,and to promote the extension of consultation and test[13].Attention should be paid to the high incidence of syphilis among sex workers,gay men,drug users and pregnant women who can serve as bridge population to transmit syphilis.In recent years,the elderly syphilis and HIV-positive persons increased year by year,also need to cause more attention.Therefore,syphilis screening and active testing are widely carried out in the outpatient and inpatient departments and maternal health institutions of medical institutions,especially the department of the voluntary HIV counselling and testing for sexually transmitted diseases.At the same time,we should continue to fully implement and consolidate the phased results of China's Plan for the Prevention and Control of Syphilis (2010-2020),constantly integrate resources for the prevention and control of syphilis and HIV/AIDS,and vigorously carry out anti-pornography activities and crack down on criminal activities such as prostitution [13,14].

However,this study has some shortcomings.Firstly,the data from the monitoring points of infectious diseases of this study were obtained from the Statistical Yearbook of China,while the data quality of individual data may not be most ideal.Additionally,the GM (1,1) model prediction used the data mathematical regularity,and could not fully take into account the impact of natural,social,environmental and other complex factors on the epidemic disease.So the possible natural,social,and environmental impact on the disease epidemic should also be comprehensively considered when making health decisions based on the predicted results [15].