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Forecasting the Incidence of Mumps in Zibo City Based on a SARIMA Model

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Forecasting the Incidence of Mumps in Zibo City Based on a SARIMA Model International Journal of Environmental Research and Public Health Article Forecasting the Incidence of Mumps in Zibo City Based on a SARIMA Model Qinqin Xu 1, Runzi Li 1, Yafei Liu 1, Cheng Luo 1, Aiqiang Xu 2, Fuzhong Xue 1, Qing Xu 2,* and Xiujun Li 1,* 1 Department of Biostatistics, School of Public Health, Shandong University, Jinan 250012, China; [email protected] (Q.X.); [email protected] (R.L.); [email protected] (Y.L.); [email protected] (C.L.); [email protected] (F.X.) 2 Shandong Center for Disease Control and Prevention, Jinan 250014, China; [email protected] * Correspondence: [email protected] (Q.X.); [email protected] (X.L.) Received: 7 July 2017; Accepted: 16 August 2017; Published: 17 August 2017 Abstract: This study aimed to predict the incidence of mumps using a seasonal autoregressive integrated moving average (SARIMA) model, and provide theoretical evidence for early warning prevention and control in Zibo City, Shandong Province, China. Monthly mumps data from Zibo City gathered between 2005 and 2013 were used as a training set to construct a SARIMA model, and the monthly mumps in 2014 were defined as a test set for the model. From 2005 to 2014, a total of 8722 cases of mumps were reported in Zibo City; the male-to-female ratio of cases was 1.85:1, the age group of 1–20 years old accounted for 94.05% of all reported cases, and students made up the largest proportion (65.89%). The main serious endemic areas of mumps were located in Huantai County, Linzi District, and Boshan District of Zibo City. There were two epidemic peaks from April to July and from October to January in next year. The fitted model SARIMA (0, 1, 1) (0, 1, 1)12 was established (AIC = 157.528), which has high validity and reasonability. The SARIMA model fitted dynamic changes of mumps in Zibo City well. It can be used for short-term forecasting and early warning of mumps. Keywords: mumps; time series analysis; SARIMA model; infectious disease epidemiology 1. Introduction Mumps is an acute respiratory infectious disease caused by the mumps virus and characterized by the inflammation of the parotid or other salivary gland. The main symptoms are nonsuppurative swollen and painful glands, low-grade fever, and headache [1,2]. Most cases of mumps are mild and self-limited, but some serious complications can also occur when the virus invaded various glandular tissue, such as the nervous system, liver, kidney and heart. Approximately 10% of mumps cases develop complications [3], with orchitis (testicular inflammation) and aseptic meningitis being the most common [1,4]. Incidents of orchitis were reported in 11.8% of male mumps patients in the Czech Republic [3]. Other complications should not also be neglected, such as pancreatitis, myositis, and oophoritis [5]. In addition, mumps usually occurs in school-age children and adolescents, and can result in childhood deafness [6]. It is also reported that the proportion of mumps cases among adults has also increased [7]. Generally, the complications would be more severe with age, and affect significantly more men than women [8]. Though cases occur in every month, mumps have obvious seasonal characteristics. Outbreak peaks from April to June and from October to January, and occurs regularly at intervals of two to five years [2]. A person would develop symptoms after direct contact with mumps patients after about two to three weeks. The disease is generally transmitted through the respiratory tract by direct contact, droplets, and saliva inhalation; the widespread non-immunized population are susceptible [5]. Int. J. Environ. Res. Public Health 2017, 14, 925; doi:10.3390/ijerph14080925 www.mdpi.com/journal/ijerph Int. J. Environ. Res. Public Health 2017, 14, 925 2 of 11 Int. J. Environ. Res. Public Health 2017, 14, 925 2 of 11 In China, mumps is defineddefined as a notifiablenotifiable infectious disease.disease. The annual incidence is more than 20/100,000 sincesince 2005; 2005; and infectionand infection rates reached rates 30/100,000 reached in30/100,000 2011 and 2012 in ( http://cdc.ncmi.cn/2011 and 2012 Share/index.jsp(http://cdc.ncmi.cn/Share/index.jsp).). Although some measures Although aimed some at measures mumps have aimed been at mumps applied, have including been applied, vaccine immunizationincluding vaccine [1], immunization the epidemic situation [1], the epidemic remains serioussituation due remains to gene serious mutation due ofto thegene mumps mutation virus of andthe mumps China’s virus huge and and China’s highly mobilehuge and population. highly mobi Outbreaksle population. have beenOutbreaks observed have in been many observed countries, in suchmany as countries, Korea in such 2013 [as9], Korea the United in 2013 States [9], the in 2006 United [10 ],States the Czech in 2006 Republic [10], the [2 Czech], the United Republic Kingdom, [2], the andUnited Belgium Kingdom, [11]. Mumpsand Belgium is extremely [11]. Mumps severe diseaseis extrem inely the severe Shandong disease province, in the andShandong it has the province, second highestand it has rate the in second respiratory highest infectious rate in respiratory diseases and infectious [12]. That diseases is a seriousand [12]. public That is health a serious concern public in Zibohealth City concern especially, in Zibo which City especially, had the highest which reportedhad the highest incidence reported of mumps incidence among of mumps the 17 cities among of Shandongthe 17 cities in of 2012 Shandong [13]. It isin necessary2012 [13]. toIt is fully necess understandary to fully the understand regularity ofthe mumps regularity in Zibo of mumps City, and in thenZibo modelCity, and and then forecast model the and disease forecast to provide the disease the scientificto provide theoretical the scientific evidences theoretical for its evidences prevention for andits prevention control. For and infectious control.disease, For infectious there are disease, many complexthere areaffecting many complex factors. affecting Time series factors. analysis Time is aseries method analysis of quantitative is a method analysis of quantitative without regardanalysis to without the influence regard of to intricate the influence factors, of and intricate it could factors, make aand scientific it could quantitative make a scientific forecast quantitative for the future forecast trends for of the the future disease trends in accordance of the disease with historicalin accordance data andwith time historical variables data [ 14and]. Thetime autoregressive variables [14]. integratedThe autoregressive moving average integrated (ARIMA) moving model average proposed (ARIMA) by Boxmodel and proposed Jenkins isby a Box commonly and Jenkins statistical is a commonly method to statis forecasttical method time series to forecast data. It time could series circumvent data. It manycould problemscircumvent in themany traditional problems regression, in the traditional such as the difficultyregression, in gettingsuch as detailed the difficulty data and in grasping getting thedetailed influencing data and factors grasping of the the forecastedinfluencing objects. factors Theof the ARIMA forecasted model objects. has beenThe ARIMA increasingly model used has inbeen epidemiologic increasingly researchused in epidemiologic to describe the research temporal to describe pattern ofthe many temporal diseases, pattern such of asmany dengue diseases, [15], tuberculosissuch as dengue [16 ,[15],17], malariatuberculosis [18] and [16,17] others, malaria [19–21 [18]]. and others [19–21]. In this this study, study, the the demographic demographic characteristics characteristics and and spatiotemporal spatiotemporal distribution distribution of mumps of mumps in Zibo in ZiboCity are City described. are described. The seasonal The seasonal ARIMA ARIMA (SARIMA) (SARIMA) model is model established is established to fit the to monthly fit the monthly mumps mumpsfrom 2005 from to 2013 2005 in to Zibo 2013 City, in Zibo and City, theand fitted the model fitted was model used was to used forecast to forecast the mumps the mumps in 2014 in to 2014 verify to verifythe applicability the applicability and feasibility. and feasibility. 2. Materials and Methods 2.1. Study Area and Data Collection ◦ 0 Zibo isis aa centralcentral citycity in in the the Shandong Shandong Province Province of of China, China, located located between between latitude latitude 35 35°5555 N′ and ◦ 0 ◦ 0 ◦ 0 3737°1717′ N,N, and and longitude longitude 117°32 117 32′ andE and 118°31 118′ E31 (FigureE (Figure 1). The1). Thecity consists city consists of nine of counties nine counties with about with about4.53 million 4.53 million permanent permanent residents, residents, according according to a demographic to a demographic census census in 2010, in 2010,and a and total a totalland landarea areaof 5965 of 5965square square kilometers, kilometers, which which covers covers nearly nearly 3.8% 3.8% of ofShandong’s Shandong’s entire entire area. area. Zibo Zibo City City has developed into an important modern industrialindustrial citycity withwith steadysteady populationpopulation growth.growth. Figure 1. The geolocation of Zibo City in Shandong Province, China (map waswas created with ArcGIS software, v. 10.2).10.2). Int. J. Environ. Res. Public Health 2017, 14, 925 3 of 11 The data on mumps from 2005 to 2014 in Zibo City are obtained from the Diseases Reporting Information System of the Shandong Center for Disease Control and Prevention, and include the age, sex and occupation for each case. The diagnostic criteria of mumps are the “Diagnostic criteria for mump” established by the Chinese Ministry of Health (http://www.moh.gov.cn/zwgkzt/ s9491/200704/38797.shtml), and the disease diagnostic criteria remained consistent during the data collection period. 2.2. Statistical Analysis We used the descriptive epidemiology method to depict the epidemical distribution of mumps firstly, including the temporal and spatial distribution, as well as sex ratio, high-incidence age group, and occupation. Given that many epidemiologic time series contain significant periodic and seasonal trends, the SARIMA model should be considered, which includes seasonal characteristics of time series [21,22].
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