Research into the resilience of the water-energy-food-ecology (WEFE) system is of great significance to ensure the safety and high quality of resources in the Yellow River Basin. To investigate WEFE system resilience and its influencing factors, this paper constructs an indicator system for WEFE system resilience based on prefecture-level city data from the Yellow River Basin spanning the years 2008 to 2021, and explores its dynamic evolution. Furthermore, this paper employs the Partial Least Squares (PLS) regression model to explore the factors influencing WEFE system resilience. It utilizes a spatial panel model to investigate the spatial spillover effects of these factors. The results indicate that WEFE system resilience in the Yellow River Basin exhibits a fluctuating upward trend. Spatially, a pattern of “low in the middle and upstream regions, high in the downstream regions” emerges. Among the driving factors, infrastructure development and the degree of innovation exhibit negative spatial spillover effects, while other factors demonstrate positive spatial spillover effects. Therefore, integrated basin management needs to be promoted by considering the systematic interlinkages of water, energy, food production and ecology and the sustainable use of resources to ensure the long-term resilience of cities. These findings provide valuable insights for policymakers to formulate more effective and coordinated resource management strategies in the Yellow River Basin, and also contributes to enriching the international literature on WEFE system research.

In this paper, we provide an effective method for estimating the thresholds of the stochastic models with time delays by using of the nonnegative semimartingale convergence theorem. Firstly, we establish the stochastic delay differential equation models for two diseases, and obtain two thresholds of two diseases and the sufficient conditions for the persistence and extinction of two diseases. Then, numerical simulations for co-infection of HIV/AIDS and Gonorrhea in Yunnan Province, China, are carried out. Finally, we discuss some biological implications and focus on the impact of some key model parameters. One of the most interesting findings is that the stochastic fluctuation and time delays introduced into the deterministic models can suppress the outbreak of the diseases, which can provide some useful control strategies to regulate the dynamics of the diseases, and the numerical simulations verify this phenomenon.