1. Epidemiological characteristics of influenza incidence
From January 1, 2016, to December 31, 2020, medical and health institutions reported 95 025 confirmed cases of influenza in Fujian Province. In the 2019 influenza outbreak, the average weekly incidence rate for the whole year was 1.8/100 000.In 2020, there was a significant reduction in the incidence of influenza compared with 2019. Except for 2019, the weekly average rate from 2016 to 2020 was between 0.50and 1.01/100 000, and the median incidence rate in each year was less than 0.42/100 000. The difference in the distribution of the incidence rate in each year was statistically significant (rank-sum test, p<0.001). The overall statistics of influenza morbidity in Fujian Province each year are presented in Table 1.
The trend of influenza incidence in Fujian Province shows obvious seasonality, with high incidence in winter. Specifically, most cases were observed from November to March each year, and the remaining months were fewer. The five-year incidence rate ranged from 0.086/100 000to 8.53/100 000, and the 95% incidence ranged from 0.17/100 000 to 5.40/100 000, with a median of 0.45/100 000 (Fig. 1 and 2).During the 2016 and 2017 winters, the influenza incidence was around 0.45/100 000. During the winter of 2018,the incidence of influenza was around 2.06/100 000, while it was above 3.27/100 000 during the 2019 and 2020 winters. The incidence of influenza in summer was found to be extremely low. Except in 2019, when the influenza outbreak, the incidence of influenza in summer generally fluctuated between 0.20/100 000to 0.30/100 000.
2. Distribution of meteorological factors
From 2016 to 2020, the temperature in Fujian Province changed significantly according to the seasons, which is characteristic of a typical subtropical climate, with a low temperature in winter and a high temperature in summer (Figure 3). Interestingly, the air temperature negatively correlated with the influenza incidence (Figure 1). In summers, temperatures were the highest, but fewer new influenza cases were observed, whereas in winters, temperatures were the lowest, but the incidence of influenza cases was the highest.
The distribution range of the weekly temperature average was between 6 and 30 °C, and the median temperature was about 19.9 °C. The shape of the violin diagram of the temperature distribution was opposite to that of the influenza incidence diagram. When the value was larger, the phenomenon of data distribution concentration occurred (Figure 4).
3. The effect of temperature on the incidence of influenza
For a better picture of the changing trend between temperature and influenza incidence, we drew a scatter plot graph (Figure 5). As presented in Figure 5 there is a clear negative correlation between temperature and influenza incidence. Specifically, when the temperatures are low, the scatter points are mainly distributed, and the influenza incidence is higher. However, when temperatures are higher, influenza incidence is relatively low:at around 30°C, the incidence rate was around 0.2/100 000. The Spearman correlation between air temperature and influenza incidence is shown in Table 2.
4. Neural Network Prediction of Temperature and Influenza Lag effect on Influenza Incidence
This retrospective study included weekly average temperatures of 265-weeks(hereinafter referred to as temperature) and influenza incidence data from 2016 to 2020. The main factor considered in the model prediction was “temperature”, and the lagged effect of the incidence of influenza was also analyzed. Different models were used for neural network training. The features of the specific models used areas follows:
4.1 Ordinary Neural Network Training (ANN)
In general, in our analyses, the closer the mean square error (MSE)value is to 0, the better the prediction ability of the model.As presented in Table 3,with the unique use of “temperature”as a factor by ANN modeling, the predicted MSE results were poor, and the number of neurons in the hidden layer had a low effect on the results. When the first-order lag of influenza incidence was considered in the analysis together with “temperature”, the prediction by ANN was significantly improved, and the number of neurons in the hidden layer had little effect on the results. Based on what precedes, when the second-order lag of influenza incidence was added, the predictive effect by ANN was further improved. When the number of neurons in the hidden layer was 5 and 10, the predictive effect was practically the best.
4.2 Deep Neural Network Training (DNN)
The results of the Deep Neural Network assay are presented in Table 4. Without regularization, the prediction ability of the optimal network by ANN was generally better than that of the DNN network. However, after regularization was applied,optimal network results by DNN and a better prediction ability were obtained. Interestingly, the best DNN network contained 11 hidden layers, with a number of 80 neurons in each hidden layer and a drop out rate of 0.1.
4.3 Recurrent Neural Network Training (RNN)
The results of the Recurrent Neural Network Training assay are presented in Table 5. The optimal network of RNN was obtained using three hidden layers, with the number of neurons in each layer of 30 and a drop out rate of 0.1. These characteristics could achieve better predictive effects than the optimal DNN network.When the number of hidden layers increased, the predictive ability of RNN decreased because the RNN network itself is relatively complex, and the number of hidden layers is prone to over-fitting. Therefore, the relatively simple 3-layer hidden layer RNN had the best predictive effect.
4.4 Gated Recurrent Unit (GRU)
Similar to the DNN network, the input variable was “temperature”, and the lag term of influenza incidence was. For this end, the dropout regularization method was used. Dropout rates of 0, 0.1, and 0.2 were respectively used in each hidden layer. Then, we considered GRUs with 3 to 11 layers, with each hidden layer containing 5 to 80 neurons. The training used a limited maximum number of training times of 1000. Overall, the network operation results are shown in Table 6. The optimal network of GRU contained three hidden layers, with 30 neurons in each layer and a drop out rate of 0.2. Under the same network structure, GRU had a stronger prediction ability than RNN. With an increase in the number of hidden layers, the prediction ability of the GRU network decreased, and the simpler GRU with three hidden layers had the best predictive effect.
In the neural network, the predictive effect when considering only “temperature” as a factor was not good with its lag because influenza is contagious, and the autocor- relation between the incidence of influenza and the incidence of the previous period is higher. Considering its infectivity and the MSE results of the neural network simulation, the temperature and influenza lag of one week and two weeks were finally selected as the input layer for the 3-layer GRU training simulation. The simulation results are shown in Figure 6. The results show that GRU has better prediction capabilities, followed by RNN, DNN, and ANN, from the utmost to the lowest, respectively.