A Network Percolation-based Contagion Model of Flood Propagation and Recession in Urban Road Networks

In this study, we propose a contagion model as a simple and powerful mathematical approach for predicting the spatial spread and temporal evolution of the onset and recession of flood waters in urban road networks. A network of urban roads resilient to flooding events is essential for provision of public services and for emergency response. The spread of floodwaters in urban networks is a complex spatial-temporal phenomenon. This study presents a mathematical contagion model to describe the spatial-temporal spread and recession process of flood waters in urban road networks. The evolution of floods within networks can be captured based on three macroscopic characteristics-flood propagation rate ($\beta$), flood incubation rate ($\alpha$), and recovery rate ($\mu$)-in a system of ordinary differential equations analogous to the Susceptible-Exposed-Infected-Recovered (SEIR) model. We integrated the flood contagion model with the network percolation process in which the probability of flooding of a road segment depends on the degree to which the nearby road segments are flooded. The application of the proposed model was verified using high-resolution historical data of road flooding in Harris County during Hurricane Harvey in 2017. The results show that the model can monitor and predict the fraction of flooded roads over time. Additionally, the proposed model can achieve $90\%$ precision and recall for the spatial spread of the flooded roads at the majority of tested time intervals. The findings suggest that the proposed mathematical contagion model offers great potential to support emergency managers, public officials, citizens, first responders, and other decision makers for flood forecast in road networks.