Stationary distribution of an SVIB Cholera model with reaction-diffusion and Brownian motion

In this study, we aimed to determine the stationary distribution of a Susceptible-Vaccine-Infected-Bacteria (SVIB) Cholera model that incorporates environmental noise and reaction-diffusion. First, we demonstrated the model's invariant set. Subsequently, a Lyapunov function was constructed to prove the existence and uniqueness of the solutions, and the model's finite-time stability was demonstrated. Furthermore, we derived the stationary distribution of the stochastic cholera model with reaction-diffusion. Finally, the theorem's results were verified through numerical simulation. Notably, the noise intensity could impact the model's stationary distribution. When the number of infected individuals and cholera bacteria decreases with reduced noise intensity, the system is characterized by a normal distribution. Therefore, appropriate measures should be taken to reduce the interference of external factors when a disease outbreak occurs.