The spread of traffic jams in urban networks has long been viewed as a complex spatio-temporal phenomenon that often requires computationally intensive microscopic models for analysis purposes. In this study, we present a framework to describe the dynamics of congestion propagation and dissipation of traffic in cities using a simple contagion process, inspired by those used to model infectious disease spread in a population. We introduce two novel macroscopic characteristics of network traffic, namely congestion propagation rate \b{eta} and congestion dissipation rate {\mu}. We describe the dynamics of congestion propagation and dissipation using these new parameters, \b{eta}, and {\mu}, embedded within a system of ordinary differential equations, analogous to the well-known Susceptible-Infected-Recovered (SIR) model. The proposed contagion-based dynamics are verified through an empirical multi-city analysis, and can be used to monitor, predict and control the fraction of congested links in the network over time.