# Neural Network Based Country Wise Risk Prediction of COVID-19
## 4 Results and Discussion
### The Effect of Weather  
To understand the effect of weather, we experimented with combining weather data. The weather data consisted of UV, minimum temperature, maximum temperature, perception, ozone, dew, and humidity. We took the mean and standard deviation for each feature. First, we combined the trend data and weather data and apply the network optimization method. Next, the optimized network was used to train and validate the results. We have verified the effect by (A) extracting the Pearson correlation coefficient among variables, (B) feature selection using ordinary least squares (OLS) regression from the combined data and finding optimized neural network, and (C) using all the features in combined data and applying the proposed method. Figure 11A shows the average Pearson correlation of all the countries among different weather data and trend. It is observed that the trend data (active case) were not significantly correlated with the different weather parameters (see the last row, i.e., yellow border). Figure 11B shows the distribution of Pearson correlation over different countries. It is noted that the weather parameters were not correlated or varied significantly. It may be possible that all the features were not linked with the prediction variable. The data contained three main concerns for the risk categorization of a country. Number of cases (\(\kappa\)), number of deaths (\(\delta\)), and number of recoveries (\(\rho\)). The number of active cases (\(\alpha\)) was calculated by \(\kappa-(\rho+\delta)\). Features were selected by backward elimination method. We calculated the p-value of all features with \(\alpha\) using ordinary least squares (OLS) regression. We employ a threshold (0.4) for choosing features. Algorithm 1 demonstrates the method. Figure 11C shows the number of times the features are selected by the countries. It is observed that choosing a lower threshold (bottom row) almost discarded all the weather data by most of the countries. Figure 12 shows the average accuracy using the proposed OLS-based feature selection, combined weather features, and without weather data. It is noted that the prediction accuracy was almost similar with and without weather data.  
\begin{table}
\begin{tabular}{c c c} \hline High Risk (HR) & Low Risk (UL) & Reaveraging (RB) \\ \hline India & Slovakia & Greenland \\ \hline USA & Malta & Uruguay \\ \hline Russia & Denmark & Zimbabwe \\ \hline Brazil & Switzerland & Japan \\ \hline Mexico & Germany & Norway \\ \hline \end{tabular}
\end{table}
Table 4: Examples of some high risk, low risk, and recovering countries based on upcoming 25 days prediction (August 2020).  
```
Input :A set of feature (\(f\)) Output :Selected set of feature (\(\hat{f}\)) Procedure Feature Selection (\(f\)=set of features)  Set \(\hat{f}=f\);  Set \(P_{threshold}=0.4\); do  Train OLS with \(\hat{f}\); \(p_{max}=\forall\hat{f}\), MAX(p-value); if\(p_{max}>p_{threshold}\)then  Remove \(\hat{f}(p_{max})\) ; while\(p_{max}>p_{threshold}\); return\(\hat{f}\)
```  
**Algorithm 1**Feature selection algorithms  
Figure 11: (**A**) Pearson correlation among features, the last row (yellow border) shows correlation with active case, (**B**) Distribution of the correlation considering all the countries, (**C**) Selected features by countries based on different thresholds.  
Figure 12: Average RMSE of total cases, recovered, and death using selected features, combined weather data, and without weather data on last 25 days prediction.