Finite-time stability of the West Nile Virus model with Brownian motion.

West Nile virus disease is an acute infectious illness caused by infection with the West Nile virus, which was first isolated from the blood of a febrile patient in the West Nile region of Uganda in 1937. In recent decades, West Nile fever has continued to expand across endemic regions globally, with no specific antiviral treatment or vaccine currently available for prevention. This study examines the finite-time stability of a stochastic West Nile virus model. Initially, the boundedness, existence and uniqueness of the solution are established. Furthermore, by constructing a Lyapunov function and utilizing the Gronwall inequality, a sufficient condition for the finite-time stability of the West Nile virus model is derived. Finally, numerical simulations are conducted to verify the theoretical results, and the influence of noise intensity, mortality rates and transmission rates on the finite-time stability of the model are analyzed. The results show that the lower the noise intensity and transmission rates, the greater the mortality rates, and the better the system can achieve finite-time stability.