SIR MODEL FOR PLANNING URBAN

To the posing of date, we came across the graphics shown below. In relation to the increase of the maximum allowed freedom in the ways of São Paulo and the second one due to reduction of the average.

In the graphs, the variables S, I and R represent, respectively: occurrences registered by the Mobile Emergency Service (SAMU), congestion of the registered routes and accidents.

For the above graph, it was noticed that with the increase of the maximum allowed speed in approximately 14%, the average time of route in the ways diminished, causing in a decrease in the congestion. On the other hand, the number of occurrences received by SAMU increased by a little over 1.5% (only on the roads).

In the second graph, it was observed that with the decrease of the maximum speed of the roads, the number of accidents decreased (12%), leading to a decrease in the number of accidents recorded by the emergency service SAMU (1%). On the other hand, it was verified that the congestion in the roads increased, due to the time of travel (14.5%).

The equations describing the observed behavior are described by the SIR model: