The objective of this study is to develop a stochastic SIRB infection model that includes general forms of infection to comprehensively analyze the dynamic behavior of cholera transmission. Specifically, we considered the influence of environmental variables on exposure rates, represented by the parameters \(\beta _{1}\) and \(\beta _{2}\) . To effectively capture the impact of stochasticity on transmission dynamics, we incorporated the Ornstein-Uhlenbeck process into the model. By constructing a Lyapunov function, we derived the stationary distribution of the model and established the conditions for extinction. Additionally, we solved the five-dimensional Fokker-Planck equation to obtain the probability density function expression at the positive equilibrium point. The results indicate that environmental factors significantly influence infection transmission. Furthermore, a comparison with the deterministic model highlights the complex nature of cholera transmission and its intrinsic stochasticity.
