Modeling conditional dependencies between recidivism and cognitive emotion regulation strategies among prisoners using a Bayesian network with interpretable summary indexes.

West Nile virus is a zoonotic disease caused by infection with the West Nile virus, primarily affecting birds, humans, and mammals such as horses and cattle. Birds serve as reservoir hosts for the virus, while humans are predominantly infected through the bites of infected mosquitoes. In 2023, cases of West Nile virus infection were reported in several countries across Europe and the United States, with Italy documenting a total of 336 cases of West Nile fever, resulting in 29 fatalities (). In 2024, multiple countries have also reported deaths attributed to West Nile virus. According to Israel¡¯s Health Ministry, 913 individuals have been confirmed infected with West Nile virus since the outbreak began in June, with a death toll reaching 70. As of September 11, Greece has recorded 162 cases of West Nile virus infection and 25 deaths. Additionally, recent West Nile virus infections have been reported in multiple European countries, including Greece, Italy, and Spain (). Currently, no specific antiviral treatment or vaccine is available to prevent the West Nile virus. The most straightforward and effective method to mitigate the risk of infection remains the avoidance of mosquito bites. Mathematical models [–] provide an effective approach for analyzing the pathogenesis of West Nile virus. For instance, Bhowmick et al. [] examined the influence of migratory bird movement patterns on the transmission dynamics of West Nile virus. Zhu et al. [] developed a West Nile virus model incorporating seasonality and investigated its dynamics along with optimal control strategies. Maliyoni [] analyzed a stochastic West Nile virus model, deriving the extinction threshold and identifying conditions that determine whether the disease persists or becomes extinct. Baafi and Hurford [] explored the effects of temperature and rainfall on disease transmission, highlighting regional differences in vector control effectiveness over time. Previous studies have primarily examined the dynamic behavior of West Nile virus using ordinary differential equation models. Concurrently, numerous researchers have developed diffusion model [–] tto further explore disease transmission. Wang et al. [] investigated the long term behavior of a West Nile virus model with free boundaries. Lin and Zhu [] incorporated the free boundaries into a reaction-diffusion West Nile model, introducing a spatio-temporal risk index. Xing et al. [] analyzed a reaction-diffusion West Nile model with spatial heterogeneity, assessing the effects of spatial variation, dispersal rates, advection rate and bird recovery rates on species survival or extinction. Chang et al. [] examined the dynamical behavior of a nonlocal diffusion West Nile virus model under spatial heterogeneity. Ge et al. []evaluated the impact of seasonal fluctuations on virus transmission. We also observe that mosquitoes and birds are highly susceptible to external disturbances. For instance: temperature, humidity, and rainfall can affect the reproductive and survival rates of mosquito vectors; insecticide spraying and vaccination campaigns face uncertainties in their implementation timing and efficacy; bird migration routes may alter disease transmission patterns. These factors collectively highlight the practical significance of investigating stochastic models to better capture the complexity and unpredictability of West Nile Virus dynamics. Up to now, there are many studies on stochastic epidemic models [,], but then, there are few papers on the dynamics of stochastic West Nile model models.