Skip to main content

Forecasting the incidence of mumps in Chongqing based on a SARIMA model



Mumps is classified as a class C infection disease in China, and the Chongqing area has one of the highest incidence rates in the country. We aimed to establish a prediction model for mumps in Chongqing and analyze its seasonality, which is important for risk analysis and allocation of resources in the health sector.


Data on incidence of mumps from January 2004 to December 2018 were obtained from Chongqing Municipal Bureau of Disease Control and Prevention. The incidence of mumps from 2004 to 2017 was fitted using a seasonal autoregressive comprehensive moving average (SARIMA) model. The root mean square error (RMSE) and mean absolute percentage error (MAPE) were used to compare the goodness of fit of the models. The 2018 incidence data were used for validation.


From 2004 to 2018, a total of 159,181 cases (93,655 males and 65,526 females) of mumps were reported in Chongqing, with significantly more men than women. The age group of 0–19 years old accounted for 92.41% of all reported cases, and students made up the largest proportion (62.83%), followed by scattered children and children in kindergarten. The SARIMA(2, 1, 1) × (0, 1, 1)12 was the best fit model, RMSE and MAPE were 0.9950 and 39.8396%, respectively.


Based on the study findings, the incidence of mumps in Chongqing has an obvious seasonal trend, and SARIMA(2, 1, 1) × (0, 1, 1)12 model can also predict the incidence of mumps well. The SARIMA model of time series analysis is a feasible and simple method for predicting mumps in Chongqing.

Peer Review reports


Mumps is a disease caused by an infection due to mumps virus. It is a vaccine-preventable toxic disease in children [1], and the main population affected is children and adolescents [2]. The clinical manifestation of mumps virus infection is pain and swelling of the parotid gland, but it may also affect various tissues and organs [3]. It can also cause serious complications, such as encephalitis, meningitis, orchitis, myocarditis, pancreatitis, and nephritis [3, 4]. Patients generally recover spontaneously within a few moments of infection, but the disease has long-term consequences, such as seizures, cerebral palsy, hydrocephalus and deafness [4, 5]. Mumps is a global epidemic [6], with outbreaks occurring in several regions, such as Ireland [7], Nebraska [8], and Arkansas [9]. The incidence of mumps in China is high [10].

In 2018, China had the highest number of cases in the world (259,071 cases), followed by Nepal (29,614 cases) and Burkina Faso (26,982 cases) [11]. From 2004 to 2018, China reported 4,272,368 cases, and the average incidence was 2144 per 100,000 per year [12]. In 1990, mumps was included in the management of class C infectious diseases (class C infectious diseases are known as surveillance and management infectious diseases, including filariasis, hydatid disease, leprosy, influenza, mumps, epidemic and endemic typhus, rubella, acute hemorrhagic conjunctivitis, hand, foot and mouth disease, and infectious diarrhoeal diseases other than amoebic dysentery, typhoid and paratyphoid, etc.) [13]. Mumps-containing vaccines were included in the expanded national immunization program in 2008 [14]. From 2014 to 2016, the reported incidence of mumps began to decline nationwide, but rose again in 2017 and 2018 [12]. Mumps is highly contagious and often causes outbreaks in school nurseries and other collective units, seriously affecting the normal school teaching order. Mumps is one of the important public health problems that endanger the physical and mental health of children and adolescents in China [15]. Thus, understanding the epidemic regularity and predicting the epidemic trend of mumps is crucial for risk analysis and health resource allocation in the health sector.

Time series analysis is a scientific quantitative prediction of the future trend of diseases based on historical data and time variables. It is a quantitative analysis method that does not consider the influence of complex factors [16]. The ARIMA model is one of the most representative and widely used models in time series prediction [17], and this method is simple and requires only endogenous variables instead of other exogenous variables. In epidemiological studies, the ARIMA model has been used in many studies, such as malaria [18], tuberculosis [19, 20], dengue [21] and other diseases [22, 23]. To the best of our knowledge, Chongqing is one of the areas with the highest incidence rates in China [24]. Furthermore, no previous research has been conducted to predict the incidence of mumps in Chongqing. To address these noted gaps, this paper is the first to establish a time series analysis of the mumps incidence data for short-term prediction in Chongqing. We developed a seasonal autoregressive comprehensive moving average (SARIMA) model to forecast the incidence of mumps. As we all know, the SARIMA model has one more seasonal effect than the ARIMA model, and it is generally handled by seasonal difference [25]. The results of this study may be useful for predicting mumps epidemics and offer reference information for mumps control and intervention in Chongqing.


Data collection

In this study, mumps data from 2004 to 2018 were collected from Chongqing CDC. All cases in each region were verified through clinical and laboratory diagnosis, and reported to the CDC by the health department. The reported data includes the sex, occupation, age and region of the patient. The data were finally collected from each region and submitted to the Chongqing CDC.

SARIMA model construction

SARIMA differs from ARIMA models in that it contains seasonal characteristics of time series [26], and is an extension of ARIMA model. The general structure of SARIMA model is expressed as SARIMA (p, d, q) × (P, D, Q)S, and its formula is as follows [27]:

$$ {\displaystyle \begin{array}{l}{\nabla}^d{\nabla}_S^D{x}_t=\frac{\Theta (B){\Theta}_S(B)}{\Phi (B){\Phi}_S(B)}{\varepsilon}_t\\ {}\Theta (B)=1-{\theta}_1B- ggg-{\theta}_q{B}^q\\ {}\Phi (B)=1-{\phi}_1B- ggg-{\phi}_p{B}^p\\ {}{\Theta}_S(B)=1-{\theta}_1{B}^S- ggg-{\theta}_Q{B}^{QS}\\ {}{\Phi}_S(B)=1-{\phi}_1{B}^S- ggg-{\phi}_P{B}^{PS}\end{array}} $$

In the above equation, B represents the backward shift operator, εt denotes the residual at time t, the mean of εt is zero and the variance of εt is constant, xt is the observed value at time t (t = 1, 2 … k). In SARIMA (p, d, q) × (P, D, Q)S, s is the length of the seasonal period, p, P, d, D, q and Q are the autoregressive order, seasonal autoregressive order, number of difference, number of seasonal difference, moving average order and seasonal moving average order, respectively [27]. According to the sequence autocorrelation function (ACF) and partial autocorrelation function (PACF) for determining the values of the six parameters in the SARIMA model. Akaike information criterion (AIC) and Schwarz Bayesian Criterion (BIC) are two indexes of model optimization. A small AIC shows that is the better fitting model [26].

Finally, two indexes were used to compare the fitting effect. The formulas for RMSE and MAPE are [28]:

$$ RMSE=\sqrt{\frac{1}{n}\sum \limits_{t=1}^n{\left({x}_t-\overset{\wedge }{x_t}\right)}^2} $$
$$ MAPE=\frac{1}{n}\sum \limits_{t=1}^n\frac{\mid {x}_t-\overset{\wedge }{x_t}\mid }{x_t} $$

In the above equation, xt is the actual incidence value, \( \overset{\wedge }{x_t} \) is the estimated incidence value, n is the number of months for forecasting. The lower RMSE and MAPE value, the better the data fitting effect.

Statistical analysis

Firstly, we used Excel 2010 to conduct a descriptive analysis of mumps in Chongqing from 2004 to 2018, and explain the sex, age, and occupational distribution of the disease onset. Secondly, the time series analysis of the mumps incidence sequence was analyzed. The “stl” function in the R 3.5.0 software was used to decompose the seasonal trend of the sequence. Finally, under the operation of the R3.5.0 software, a SARIMA model was established to predict the incidence of mumps. In this study, the incidence of mumps from 2004 to 2017 was used as a training dataset to fit the SARIMA model, predict the incidence of mumps in 2018, and verify the predicted effect. The significance level was p < 0.05.


The monthly incidence of mumps number is presented in Fig. 1, showing that monthly mumps incidence was low in February and peaked in April to July. Table 1 shows the top five regions with the highest number of mumps in Chongqing in the past 15 years. Although the location of Chongqing has changed, it is mainly concentrated in the northeast and west of Chongqing. Table 2 shows reported 159,181 mumps cases in the past 15 years (2004–2018), in Chongqing, The cases included 93,655 males and 65,526 females (male-to-female ratio of 1.43:1), with mumps commonly occurring between the ages of 0 and 19, and the age group of 0–19 years accounted for the 92.41% (n = 147,094) of all reported cases. The group with the highest proportion of mumps is students, amount to 62.83% (n = 100,013), followed by scattered children and children in kindergarten.

Fig. 1
figure 1

Monthly incidence of mumps from 2004 to 2018 in Chongqing

Table 1 The top five regions with more mumps cases each year in Chongqing from 2004 to 2018
Table 2 Distribution of mumps by sex, age and occupation in Chongqing from 2004 to 2018

SARIMA (p, d, q) × (P, D, Q)s model

Figure 2 shows the sequence diagram of mumps, and the sequence is nonstationary. Furthermore, the monthly incidence of mumps in Chongqing suggested a slightly decreasing tendency and seasonal tendency. Figure 3 shows the decomposition diagram of the sequence, with an obvious seasonality. After the natural logarithm transformation of the original data, a one-step difference and seasonal difference with a period of 12 was conducted to remove non-stationarity. The sequence diagram after the difference was stationary (Fig. 4), and the ADF test results showed that the sequence was stationary (p < 0.05). Figure 5 shows that ACF and PACF of the sequence were both trailing. Considering that the value of p, q, P and Q generally does not exceed 2, a trial order from 0 to 2 was performed. Only five models passed the test and the model parameter test: SARIMA(1, 1, 1) × (1, 1, 0)12, SARIMA(0, 1, 2) × (1, 1, 0)12, SARIMA(1, 1, 1) × (0, 1, 1)12, SARIMA(2, 1, 1) × (0, 1, 1)12, SARIMA(1, 1, 2) × (0, 1, 1)12. The AIC, BIC values, and two error indicators of the five models were compared in Table 3. And the SARIMA(2, 1, 1) × (0, 1, 1)12 model was selected as the best one.

Fig. 2
figure 2

Reported monthly incidence of mumps from January 2004 to December 2017

Fig. 3
figure 3

Trend, seasonal and residual components derived from STL decomposition of monthly mumps incidence for Chongqing during 2004–2018

Fig. 4
figure 4

Sequence diagram after a 1-step difference and seasonal difference with a period of 12

Fig. 5
figure 5

Autocorrelation function (ACF) and partial ACF charts of monthly mumps incidence numbers. a ACF chart; b Partial ACF chart

Table 3 AIC values, BIC values, RMSE and MAPE for different SARIMA models

Table 4 shows the estimated and standard errors of model parameters and their corresponding significance values. The model equation is given as

$$ \nabla {\nabla}^{12}{x}_t=\frac{1-0.8197B}{1-0.7186B+0.2305{B}^2}\left(1-0.7643{B}^{12}\right){\varepsilon}_t\kern0.5em ,{\varepsilon}_t\sim N\left(0,0.062\right) $$
Table 4 Estimates and standard error of SARIMA(2, 1, 1) × (0, 1, 1)12 model parameters

The SARIMA(2, 1, 1) × (0, 1, 1)12 model was used to forecast the incidence of mumps in 2018. Table 5 shows the value of prediction, RMSE and MAPE values are 0.9950 and 39.8396%, respectively. The actual value of incidence and fitted incidence of SARIMA model monthly are shown in Fig. 6. Figure 6 and Table 5 show that the tendency and epidemics from predicted incidence are close to actual value of incidence and epidemic circumstance of mumps.

Table 5 Reported and forecasted incidence of mumps for 2018
Fig. 6
figure 6

SARIMA(2, 1, 1) × (0, 1, 1)12 model fitting, verification and forecasting of mumps incidence in Chongqing from January 2004 to December 2018. The black asterisk represents the actual value, the red dotted line represents the fitting value, and the blue dotted line represents the 95% confidence interval. Actual Data; SARIMA Model Fitting Values; 95%Confidence Line


In this study, we found that the annual incidence of mumps decreased significantly from 2004 to 2007 and increased from 2007 to 2011. The lowest incidence was in 2007 (175,463/100000) and the highest was in 2011 (591,471/100000). In the 159,181 reported cases, males were 1.43 times as many as females. These findings are consistent with the results of relevant literature [29]. In terms of age and occupation, the largest proportion of mumps cases were 0–19 years old (92.41%) and students (62.83%), indicating that children and students are the main targets of protection. In addition, this study shows that the western and northeastern of Chongqing are high-incidence areas (Table 1). Therefore, the government should strengthen the prevention and control measures of mumps in important areas and populations.

We decomposed the mumps incidence sequence and found that the mumps incidence sequence had obvious trends and seasonality, the monthly incidence of mumps was low in February and peak in April to July, which was consistent with previous studies [10, 30]. Therefore, taking some interventions are necessary to reduce the spread of infectious diseases in public transportation from April to July.

The results of this study indicate that model SARIMA(2, 1, 1) × (0, 1, 1)12 is the best predictive model. Figure 6 shows the 95% CIs of the forecast value in this paper containing all of the real observed data, which is a good match between the observed value and the fitted value. The incidence of mumps in 2018 peaked from April to June but showed a decreasing trend after June due to the reduction of students’ contact during the summer vacation. Thus far, in terms of infectious diseases, the SARIMA model has good results in predicting hand, foot, and mouth disease [31] and tuberculosis [32]. This study is the first to use the SARIMA model to analyze the incidence of mumps in Chongqing. The SARIMA(2, 1, 1) × (0, 1, 1)12 model in this study can well reflect the incidence of mumps in Chongqing, and has a good short-term predictive effect. It can provide early warning to health authorities to formulate plans and implement public health intervention measures to prevent and control the disease.

Compared with the ARIMA model, the SARIMA model increases the seasonal effect and is suitable for analyzing sequences with obvious seasons and periodicity [33], while most epidemiological data are seasonal and periodic [32, 34,35,36]. Compared with other time series analysis methods, The SARIMA model generally adopts the logarithm method, difference method and the seasonal difference method [37, 38] to make the series stable without the need for complicated conversion or variable substitution [39, 40]. In addition, related research shows that among various time series analysis methods, ARIMA is a useful tool for interpreting surveillance data for disease prevention and control [41, 42].

This study has several limitations. We only made short-term predictions. Therefore, various factors affecting the incidence of mumps should be considered to establish a long-term and stable prediction model. In future research, hybrid models, such as the SARIMA-NAR hybrid model [43], SARIMA-NARNNX hybrid model [44], and SARIMA-NARX hybrid model [45], can be used to analyze or predict diseases.


The results of this study suggest that applying the ARIMA time series models to forecast the incidence of mumps is feasible. The confidence intervals of the predicted values contain all the actual values. Thus, the SARIMA(2, 1, 1) × (0, 1, 1)12 model may be used to predict the incidence of mumps. The short-term prediction of mumps is effective, which is helpful for the evaluation of prevention or control measures. Meanwhile, timely and effective countermeasures can be adopted for the epidemic peak that may occur. For instance, the government has strengthened publicity on mumps prevention and control knowledge to improve the public’s awareness of the disease.

Availability of data and materials

The data that support the findings of this study are available from the Chongqing Municipal Center for Disease Control and Prevention, but restrictions apply to the availability of these data, which were used under license for the current study, and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of Chongqing CDC.



Seasonal autoregressive integrated moving average


Root mean square error


The mean absolute percentage error


Akaike Information Criterion


Schwarz Bayesian Criterion


  1. Hviid A, Rubin S, Muhlemann K. Mumps. Lancet. 2008;371:932–44.

    Article  Google Scholar 

  2. Rubin S, Eckhaus M, Rennick LJ, Bamford CG, Duprex WP. Molecular biology, pathogenesis and pathology of mumps virus. J Pathol. 2015;235:242–52.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  3. Betakova T, Svetlikova D, Gocnik M. Overview of measles and mumps vaccine: origin, present, and future of vaccine production. Acta Virol. 2013;57:91–6.

    CAS  Article  PubMed  Google Scholar 

  4. Rubin S, Kennedy R, Poland G. Emerging mumps infection. Pediatr Infect Dis J. 2016;35:799–801.

    Article  Google Scholar 

  5. KWaKL G. Measles, mumps, rubella vaccine (Priorix™; GSK-MMR) a review of its use in the prevention of measles, mumps and rubella. Adis Data Inf BV. 2003;63:19.

    Article  Google Scholar 

  6. Kaaijk P, Gouma S, Hulscher HI, Han WG, Kleijne DE, van Binnendijk RS, van Els CA. Dynamics of the serologic response in vaccinated and unvaccinated mumps cases during an epidemic. Hum Vaccin Immunother. 2015;11:1754–61.

    Article  PubMed  PubMed Central  Google Scholar 

  7. Ferenczi A, Gee S, Cotter S, Kelleher K, On Behalf Of The Mumps Outbreak Control T. Ongoing mumps outbreak among adolescents and young adults, Ireland, august 2018 to January 2020. Euro Surveill. 2020;25.

  8. Donahue M. Multistate mumps outbreak originating from asymptomatic transmission at a Nebraska wedding — six states, august–October 2019. Morb Mortal Wkly Rep. 2020;69:666–9.

    Article  Google Scholar 

  9. Pike J, Marin M, Guo A, Haselow D, Safi H, Zhou F. 2016-2017 Arkansas mumps outbreak in a close-knit community: assessment of the economic impact and response strategies. Vaccine. 2020;38:1481–5.

    Article  PubMed  Google Scholar 

  10. Cui A, Zhu Z, Hu Y, Deng X, Sun Z, Zhang Y, Mao N, Xu S, Fang X, Gao H, et al. Mumps epidemiology and mumps virus genotypes circulating in mainland China during 2013-2015. PLoS One. 2017;12:e0169561.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  11. Mumps Reported cases by country. Availabe online: (Accessed on 19 Jul 2018).

  12. Jiang RJ, Yin QZ, Xu MJ, Zhao ZM, Deng Y, Che YC. Epidemiological characteristics of mumps in mainland China from 2004 to 2018 and key population for prevention and control. Chin J Contemp Pediatr. 2019;21:441–4.

    Article  Google Scholar 

  13. Yu X. Epidemiological features and prevention strategies of mumps in China. Modern Prev Med. 2015;42:2689–91.

    Google Scholar 

  14. The National Health Commission, PRC expanded the implementation programme of the National Immunization Program.

  15. Chen DC, Chen ZF, Yang XH, Pan WY, Wang Q, Zhang SH, Zheng NX, Huang LF, Zhou Y. Epidemiological and pathogenic characteristics of mumps in Fujian province, 2005-2017. Chin J Epidemiol. 2018;39:1356–61.

    Article  Google Scholar 

  16. Wu JB, Ye LX, You EK. Application of ARIMA model in predicting the incidence of infectious diseases. J Math Med. 2007;20:90–2.

    Article  Google Scholar 

  17. Li JF, Zong Q. The forecasting of the elevator traffic flow time series based on ARIMA and GP. Adv Mater Res. 2012;588-589:1466–71.

    Article  Google Scholar 

  18. Kumar V, Mangal A, Panesar S, Yadav G, Talwar R, Raut D, Singh S. Forecasting malaria cases using climatic factors in Delhi, India: a time series analysis. Malar Res Treat. 2014;2014:482851.

    Article  PubMed  PubMed Central  Google Scholar 

  19. Moosazadeh M, Nasehi M, Bahrampour A, Khanjani N, Sharafi S, Ahmadi S. Forecasting tuberculosis incidence in Iran using box-Jenkins models. Iran Red Crescent Med J. 2014;16:e11779.

    Article  PubMed  PubMed Central  Google Scholar 

  20. Wang H, Tian CW, Wang WM, Luo XM. Time-series analysis of tuberculosis from 2005 to 2017 in China. Epidemiol Infect. 2018;146:935–9.

    CAS  Article  PubMed  Google Scholar 

  21. Martinez EZ, Silva EASD, Fabbro ALD. A SARIMA forecasting model to predict the number of cases of dengue in Campinas, state of São Paulo, Brazil. Rev Soc Bras Med Trop. 2011;44:436–40.

    Article  PubMed  Google Scholar 

  22. Lin Y, Chen M, Chen G, Wu X, Lin T. Application of an autoregressive integrated moving average model for predicting injury mortality in Xiamen, China. BMJ Open. 2015;5.

  23. Picardeau M, et al. Burden of disease measured by disability-adjusted life years and a disease forecasting time series model of scrub typhus in Laiwu, China. PLoS Negl Trop Dis. 2015;9:e3420.

    CAS  Article  Google Scholar 

  24. Fei FR, Feng LZ, Xu Z, Feng ZJ. Epidemiology of mumps in China, 2008-2010. Surveill Infect Dis. 2011;26:691–3.

    Article  Google Scholar 

  25. Qiu H, Zeng D, Yi J, Zhu H, Hu L, Jing D, Ye M. Forecasting the incidence of acute haemorrhagic conjunctivitis in Chongqing: a time series analysis. Epidemiol Infect. 2020;148:e193.

    Article  Google Scholar 

  26. Peng Z-X. ARIMA multiplicative seasonal module and its application in the prediction of infectious diseases. Appl Stat Manag. 2008;27:362–8.

    Article  Google Scholar 

  27. Cao S, Wang F, Tam W, Tse LA, Kim JH, Liu J, Lu Z. A hybrid seasonal prediction model for tuberculosis incidence in China. BMC Med Inform Decis Mak. 2013;13:56.

    Article  PubMed  PubMed Central  Google Scholar 

  28. Mohammed SH, Ahmed MM, Al-Mousawi AM, Azeez A. Seasonal behavior and forecasting trends of tuberculosis incidence in holy Kerbala, Iraq. Int J Mycobact. 2018;7:361–7.

    Article  Google Scholar 

  29. Zhu H, Zhao H, Qu R, Xiang HY, Hu L, Jing D, Sharma M, Ye ML. Epidemiological characteristics and spatiotemporal analysis of mumps from 2004 to 2018 in Chongqing, China. Int J Environ Res Public Health. 2019;16:3052.

    Article  PubMed Central  Google Scholar 

  30. Su QR, Liu J, Ma C, Fan CX, Wen N, Luo HM, et al. Epidemic profile of mumps in China during 2004–2013. Zhonghua yu fang yi xue za zhi [Chin J Prev Med]. 2016;50(7):611–4.

    CAS  Article  Google Scholar 

  31. Tian CW, Wang H, Luo XM. Time-series modelling and forecasting of hand, foot and mouth disease cases in China from 2008 to 2018. Epidemiol Infect. 2019;147:e82.

    CAS  Article  Google Scholar 

  32. Mao Q, Kai Z, Wu Y, Chaonan C. Forecasting the incidence of tuberculosis in China using the seasonal auto-regressive integrated moving average (SARIMA) model. J Infect Public Health. 2018;11:707–12.

    Article  PubMed  PubMed Central  Google Scholar 

  33. Valipour M. Long-term runoff study using SARIMA and ARIMA models in the United States. Meteorol Appl. 2015;22:592–8 [CrossRef].

    Article  Google Scholar 

  34. Wang Y, Xu C, Zhang S, Yang L, Wang Z, Zhu Y, Yuan J. Development and evaluation of a deep learning approach for modeling seasonality and trends in hand-foot-mouth disease incidence in mainland China. Sci Rep. 2019;9:8046.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  35. Cong J, Ren M, Xie S, Wang P. Predicting seasonal influenza based on SARIMA model, in mainland China from 2005 to 2018. Int J Environ Res Public Health. 2019;16.

  36. Liu H, Li C, Shao Y, Zhang X, Zhai Z, Wang X, Qi X, Wang J, Hao Y, Wu Q, Jiao M. Forecast of the trend in incidence of acute hemorrhagic conjunctivitis in China from 2011-2019 using the seasonal autoregressive integrated moving average (SARIMA) and exponential smoothing (ETS) models. J Infect Public Health. 2020;13:287–94.

    Article  PubMed  Google Scholar 

  37. Li RZ, Zhang T, Liang YM, Luo C, Jiang Z, Xue FZ, Liu YZ, Liu J, Li XJ. Application of SARIMA model in the prediction of mumps. J Shandong Univ (Medical Edition). 2016;54:82–6.

    Article  Google Scholar 

  38. Gharbi M. Time series analysis of dengue incidence in Guadeloupe, French West Indies: forecasting models using climate variables as predictors. BMC Infect Dis. 2011;11:166.

    Article  PubMed  PubMed Central  Google Scholar 

  39. Liu X, Jiang B, Bi P, Yang W, Liu Q. Prevalence of haemorrhagic fever with renal syndrome in mainland China: analysis of National Surveillance Data, 2004-2009. Epidemiol Infect. 2012;140:851–7.

    CAS  Article  PubMed  Google Scholar 

  40. Shumway RH, Stoffer DS. Time series analysis and its applications: with R examples. 3th ed. New York: Springer; 2011. p. 83e162.

    Book  Google Scholar 

  41. Ma L, Tian F. Application of time series analysis in the prediction of hypertension incidence. Chin J Gerontol. 2010;30:1777–80.

    Google Scholar 

  42. Feng H, Duan G, Zhang R, Zhang W. Time series analysis of hand-foot-mouth disease hospitalization in Zhengzhou: establishment of forecasting models using climate variables as predictors. PLoS One. 2014;9(1):e87916.

    Article  Google Scholar 

  43. Wang Y, Xu C, Wang Z, Zhang S, Zhu Y, Yuan J. Time series modeling of pertussis incidence in China from 2004 to 2018 with a novel wavelet based SARIMA-NAR hybrid model. PLoS One. 2018;13:e0208404.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  44. Wang Y, Xu C, Zhang S, Wang Z, Yang L, Zhu Y, Yuan J. Temporal trends analysis of tuberculosis morbidity in mainland China from 1997 to 2025 using a new SARIMA-NARNNX hybrid model. BMJ Open. 2019;9:e024409.

    Article  PubMed  PubMed Central  Google Scholar 

  45. Wang Y, Xu C, Wang Z, Yuan J. Seasonality and trend prediction of scarlet fever incidence in mainland China from 2004 to 2018 using a hybrid SARIMA-NARX model. PeerJ. 2019;7:e6165.

    Article  PubMed  PubMed Central  Google Scholar 

Download references


The authors express their thanks to the Chongqing Municipal Center for Disease Control and Prevention for the disease data as well as the help from teachers of Chongqing Medical University.


This research received no external funding.

Author information

Authors and Affiliations



H.Q.(Hongfang Qiu) and H.Z.(Han Zhao) contributed equally to this paper. Conceptualization, M.Y.; Methodology, H.Q. (Hongfang Qiu) and H.Z. (Han Zhao); Software, H.Q. (Hongfang Qiu); Validation, R.O.; Formal analysis, H.Q. (Hongfang Qiu); Investigation, H.Q. (Hongfang Qiu) and H.Z. (Han Zhao); Resources, H.Z. (Han Zhao); Data curation, L.H. and H.Z.; Writing—original draft preparation, H.Q. (Hongfang Qiu); Writing—review and editing, H.Q. (Hongfang Qiu), R.O., H.X. and M.Y.; Visualization, H.Z. and L.H.; Supervision, M.Y., and R.O.; Project administration, M.Y. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Mengliang Ye.

Ethics declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no conflict of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit The Creative Commons Public Domain Dedication waiver ( applies to the data made available in this article, unless otherwise stated in a credit line to the data.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Qiu, H., Zhao, H., Xiang, H. et al. Forecasting the incidence of mumps in Chongqing based on a SARIMA model. BMC Public Health 21, 373 (2021).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI:


  • Incidence
  • Mumps
  • SARIMA model
  • Chongqing