SIR model analysis of traffic congestion dynamics in urban areas

Abstract

In highway traffic flows, where most vehicles pass over flyovers to bypass congestion at the macro level, there is a close relationship with the spread of infectious diseases, which are most commonly modeled using the susceptible-infected-recover(SIR) model. To smoothen traffic flow, a control variable is introduced that will be optimized, in this case, the duration of the green light at an intersection. Stability behavior of equilibrium points, reproduction number \(\mathcal{R}_0\), and its effect on the three compartments. The numerical simulations were verified to confirm the previous results. The behavior of the three compartments with respect to the \(\mathcal{R}_0\) value was obtained. The numerical simulation results also showed the positive impact of the duration of the green light on vehicles affected by traffic congestion.