Risky driving behavior propagation: A novel stochastic SIR model and two-stage risk quantification method

Risky driving behavior (RDB) can cause panic and anger among other drivers. Under the influence of irrational emotions, RDB can reoccur, resulting in a phenomenon known as risky driving behavior propagation (RDBP). RDBP is a dangerous phenomenon, which can easily lead to traffic conflicts and accidents. It is significant to determine the propagation mechanism of RDBP to road safety. Firstly, RDBP can be considered a type of disease because three essential components of RDBP share similarities with an epidemic. A stochastic SIR model for risky driving behavior propagation (SSIR-RDBP) is constructed to quantify the mechanism of RDBP. Additionally, a Lyapunov function is adopted to prove the existence and uniqueness of the model solution. Secondly, based on current moment risk and cumulative risk, a two-stage risk approach is adopted to quantify the risk of RDBP. The Conditional Value at Risk (CVaR) is used to quantify the current moment risk, and the probability of the Markov state transition matrix is introduced to describe the cumulative risk. Finally, sensitivity analysis of the model parameters is carried out to explore the intrinsic variables of the parameters. The results suggest that the risk of RDBP increases rapidly to its peak value within the first 5 s. As traffic saturation increases, the decline rate of sustainable drivers and the rise rate of recovered individuals grows cubically, and the rate of reaching peak infection increases linearly. Furthermore, the fluctuation range of risk and the maximum risk both increase quadratically. The driver’s emotional control ability is strongest when the infection rate is set to 4, and the recovery rate increases linearly with road safety education. Improving the driver’s emotional control ability, and increasing awareness of road safety education, can help to control the risk in RDBP.