Resumen
The risk transmission mechanisms of urban river ecological management engineering projects are examined in this study. Using the Susceptible Exposed Infectious Recovered Susceptible (SEIRS) model for risk transmission, a model of risk propagation delay for urban river ecological management engineering projects on scale-free networks is developed, which takes into account the effects of risk propagation and delay. We conducted a steady-state analysis of the model and obtained the basic reproduction number R. When R > 1, the equilibrium point of risk outbreak is stable, and when R < 1, the equilibrium point of risk disappearance is stable. Numerical simulations of the model were conducted using the MATLAB2022b to reveal the dynamic propagation patterns of risk in urban river ecological management engineering projects. The research results show that the steady-state density of the infected nodes in the network increases with the increase in the effective propagation rate and the propagation delay time; the propagation delay reduces the risk propagation threshold in the network and accelerates the occurrence of the equilibrium state of risk outbreak. There is a correlation between the transmission rate of latent nodes and the transmission rate of infected nodes, and the effective transmission rate of latent nodes has a greater influence on risk propagation. The spread of risk in the network can be effectively controlled and mitigated with targeted immunity for susceptible nodes. This article, based on the theory of complex networks and the mean-field theory, takes into account the propagation delay and spreading of latent nodes. Building a D-SEIRS model for risk propagation broadens the research perspective on urban river ecological management risk propagation.