Traffic congestion is a common problem in cities all around the world. It causes losses in terms of time, money and pollution, and dampens the functionality of the transportation infrastructure, critical in the context of catastrophes such as earthquakers, wildfires and others. Planning for transportation systems which are resilient to traffic congestion is essential for cities. Modeling daily traffic patterns can help by allowing to explore the effect of actions looking to palliate its effect. However, modeling traffic can be challenging, as available models are highly complex both in terms of calibration and computation. Recently, scientists have started to consider the use of simple compartmental models like the SIR (Susceptible-Recovered-Infected) to describe daily traffic congestion in terms of spreading and recovery rates. While the resulting description provides an overall picture of the dynamics, it is extremely aggregated, disregarding differences across space completely.

Here we consider the use of spatially distributed SIR models for describing daily traffic congestion. We model traffic congestion in a region by splitting it into subregions of interest, and consider coupled spreading dynamics among them. This leads to a coupled set of differential equations that allows capturing differences across subregions. To calibrate these models we use realistic traffic conditions produced with the traffic microsimulator SUMO, and phone-based mobility information from the San Francisco Bay Area in the US. We consider multiple scales by splitting the region into different numbers of subregions in a hierarchical way (and thus subregions at finer scales are contained in subregions at coarser scales) using the uber h3 library. However, as we move into smaller subregions of the order of thirty square kilometers, the number of parameters becomes too large to allow for calibration solely based on data. Taking inspiration in the mean-field approach, we regularize the fitting at different levels by linking the spreading coefficients of a given subregion with its direct parent. The mean field approach allows obtaining analytical approximations linking the spreading and recovery rates of a region and its children subregions.

The resulting framework allows for a modeling approach that is consistent through different scales, allowing for faster calibration and reduced error. By applying the framework to traffic in San Francisco, we study which subregions affect the most the overall traffic congestion, and how they affect each other. The results move a step forward in the potential of the use of compartmental models for congestion reduction planning.