Impact of COVID-19 outbreaks and interventions on influenza in China and the United States

Coronavirus disease 2019 (COVID-19) was detected in China during the 2019–2020 seasonal influenza epidemic. Non-pharmaceutical interventions (NPIs) and behavioral changes to mitigate COVID-19 could have affected transmission dynamics of influenza and other respiratory diseases. By comparing 2019–2020 seasonal influenza activity through March 29, 2020 with the 2011–2019 seasons, we found that COVID-19 outbreaks and related NPIs may have reduced influenza in Southern and Northern China and the United States by 79.2% (lower and upper bounds: 48.8%–87.2%), 79.4% (44.9%–87.4%) and 67.2% (11.5%–80.5%). Decreases in influenza virus infection were also associated with the timing of NPIs. Without COVID-19 NPIs, influenza activity in China and the United States would likely have remained high during the 2019–2020 season. Our findings provide evidence that NPIs can partially mitigate seasonal and, potentially, pandemic influenza.


Supplementary note 1: Data collation and analysis
The influenza laboratory test positive rate for each epidemic week was used to define the intensity of influenza activity. Influenza activity intensity levels were determined by the epidemic weeks in the winter-spring seasons in China and the United States (US). Epidemiological characteristics of influenza vary across China due to geographical differences between the North and the

Supplementary note 2: Polynomial curves fitting
Curve fitting is the process of constructing a curve or mathematical function that has the best fit to a series of data points, subject to constraints. The order of the equation is a third degree polynomial: First, the influenza test positive rate in 2011-2019 winter-spring epidemic week was calculated to determine the season corresponding to high, moderate, and low activity intensities described above.
Second, curve fitting functions in SPSS22.0 and SAS JMP Pro 14 were used to fit influenza activity levels at each intensity for southern China, northern China, and the US (Supplementary Fig. 1 and Table S1).  at is a white noise process.

Basic principles
The data sequence formed by the predicted object over time is regarded as a non-random sequence. A time series is a group of time-dependent variables 3 .
The dependence or auto-correlation of this group of variables represents the continuity of the development of the predicted object. Once this autocorrelation is described by the corresponding mathematical model, the future value can be predicted from the past and present values of the time series 4 .

Formula
The general expression of the ARIMA model is ARIMA (p, d, q) (P, D, Q) s, 5 where p and q are the auto-regressive (AR) and moving average (MA) orders, and P and Q seasonal auto-regression and moving average order, d, D are the difference order and seasonal difference order, s is the seasonal period 5,6 . falls outside the confidence interval, in which case we need to smooth the data to be a stationary by making a difference 9 . A non-stationary series with seasonality into a stationary one by using the transformation:

Modeling steps
where D is the number of seasonal differences and d is the number of regular differences.
With a 1-time non-seasonal difference and a 1-time seasonal difference, the sequence non-stationarity was eliminated with white noise. Ljung-Box test determined the Sequence to be non-random (p<0.05).
② Model identification. We determined the model parameters, referring to the sequence scatter plot, auto-correlation function (ACF) plot, and partial auto-correlation function (PACF) plot (Figs. S7-S8). We used Akaike information criterion (AIC) and decision coefficient R 2 from all candidate models to identify the best p and q values, and then determined the parameters P and Q step-by-step 10 .
③ Model estimation and validation. We performed a Q test on the residuals to check the autocorrelation of the residuals (Supplementary Fig. 9). If the residuals have no autocorrelation, the model fits well 11 . AIC. The larger the R 2 , the smaller the AIC, the better the fit (Table S2). Northern China. c the US. Supplementary Fig. 3. Stationarity test.