Data source
We obtained data from the official website of Health Commission of Sichuan Province (http://wsjkw.sc.gov.cn/). The number of mumps cases per month was reported from January 2017 to July 2020. Data used in this study are available in the Supplementary Materials.
Non-pharmaceutical interventions against COVID-19
The first confirmed COVID-19 case from Wuhan in Sichuan was reported on January 21, 2020, and emergency response to major public health events in Sichuan upgraded to level 1 (the highest level) on January 24, 2020. A series of non-pharmaceutical interventions against COVID-19 were implemented, including social distancing, contact tracking, personal protection, travel restriction, etc. First, school holidays were extended, and schools were not allowed to open without permission of the local government, especially the kindergarten and primary school. Second, mass gatherings and major public events were canceled, and people were encouraged to stay at home as much as possible. Third, personal protective behaviors became normalized, such as hand washing and face masks. Additionally, the local government organized environmental disinfection in public places. Continuous rigorous social and public health measures could effectively decrease the spread of mumps.
Model construction
We modelled mumps incidence per month in Sichuan using the seasonal autoregressive integrated moving average (SARIMA) model, ARIMA (p, d, q) × (P, D, Q) S given by:
![](data:image/png;base64,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)
where p is the AR order, d is the degree of differencing, q is the MA order; P is the seasonal AR order, D is the degree of seasonal differencing, Q is the seasonal MA order, and S is the length of the seasonal period; B is the backshift operator.
Figure 1 showed the modelling process. We divided all data into three intervals: training interval (01/2017-06/2019), testing interval (07/2019-12/2019), and projecting interval (01/2020-12/2020). The stationarity of time series was judged by the Augmented Dickey-Fuller (ADF) test, and white noise was judged by the Ljung-Box test. We estimated d and D based on the time series diagram and ADF test. Next, we identified parameters p, d, Q, D by the autocorrelation function (ACF) and partial autocorrelation function (PACF), and optimized parameters by Akaike information criterion (AIC). Finally, residuals were diagnosed as white noise by the Ljung-Box test. All analyses were done using R software version 4.0.2. Code used in this study is available in the Supplementary Materials.
Model prediction and assessment
We projected the monthly incidence of mumps from July 2019 to December 2020. The projecting precision of the model was assessed by calculating the mean absolute percentage error (MAPE) between the reported cases and projected cases from July 2019 to December 2019. We compared the monthly number of mumps cases reported in 2020 against the average from corresponding periods in the preceding years (2017-2019) and the projected values by the SARIMA model. We performed a monthly one-sided (less) paired difference t-test using R version 4.0.2[6]. We calculated the percent change with 95% confidence interval (95%CI) in mumps cases reported in 2020 compared with the projected values using the Wilson method[11].