# Analysing Urban Traffic Patterns with Neural Networks and COVID-19 Response Data
## 4 Results
### Results of Modelling  
As mentioned earlier, the mobility model during the COVID-19 pandemic period was created using the neural network. We constructed the modelling stream in the IBM SPSS Modeler software, presented in Figure 13.  
Each \"yellow diamond\" in the figure represents one neural network model for a given type of vehicle. Additionally, on the left side, there is a comprehensive model containing all types of vehicles and both directions. The models are not constructed separately for individual sensors but include the sensor as one of the explanatory variables. Since a neural network model is generally considered a \"black box\", it is impossible to precisely interpret the model results in terms of relationships between input data, neural network layers, and the model's output in the form of predictions. It would be possible to describe the strength of the relationship, but there are many such relationships in a neural network, leading to a loss of clarity in interpreting the results. An example of a neural network model is shown in Figure 14, representing a model for cars entering the city centre (cars_in). Therefore, instead of interpreting each relationship, we focused on the importance of predictors (explanatory variables) in the created models [39; 60]. This information is crucial for demonstrating the pandemic's impact and implementing anti-pandemic measures on city mobility. In each neural network model, it is possible to illustrate the importance of predictors along with their significance in the model. Figure 15 shows the predictor importance for the comprehensive mobility model. The model includes other explanatory variables apart from those depicted, but for the figure, we have only included those that are significant in the model at the chosen significance level. The importance is calculated so that the cumulative importance of all the explanatory variables used in the model is one. Figure 13: Modelling stream of mobility. Among the most important variables (in the order of importance) in the model are the following:  
* Sensor number (variable name _sensor_) was used as one of the explanatory variables to avoid creating a model for each sensor separately; this variable has the highest importance in the model. * Month of the year (variable name _month_); its presence among the important variables suggests changes in mobility throughout the year. * Day of the week (variable name _day of the week_); its presence suggests changes in mobility throughout the week. * Time (variable name _time_) divided into 15-min intervals during the day; the presence of this variable in the model confirms that vehicle numbers vary significantly throughout the day. Figure 14: A neural network model for the number of cars in the direction to the city centre (_cars_in_). Figure 15: Predictor importance in the comprehensive mobility model. * Number of confirmed deaths during the COVID-19 pandemic (variable name _confirmed deaths_), cancellation of public events during the pandemic (variable name _cancel public events_), number of confirmed cases (variable name _confirmed cases_), containment health index during the pandemic (variable name _containment health index_), and restrictions on gatherings during the pandemic (variable name _restrictions on gatherings_). The presence of the variables mentioned above related to the COVID-19 pandemic in the model demonstrates the significant impact of the pandemic and the implemented anti-pandemic measures on vehicle numbers in the city. The neural network model created in this way, with the automatic selection of variables with the greatest impact on vehicle numbers, has shown that mobility was significantly influenced by the course of the pandemic and the level of implemented measures. There are still other variables in the model, but they are not of such importance, so they are not included in the previous figure. We also created individual neural network models for each type and direction of the vehicle.