Dynamical behavior of a stochastic dengue model with Ornstein–Uhlenbeck process

We develop and study a stochastic dengue model with Ornstein–Uhlenbeck process, in which we assume that the transmission coefficients between vector and human satisfy the Ornstein–Uhlenbeck process. We first show that the stochastic system has a unique global solution with any initial value. Then we use a novel Lyapunov function method to establish sufficient criteria for the existence of a stationary distribution of the system, which indicates the persistence of the disease. In particular, under some mild conditions which are applied to ensure the local asymptotic stability of the endemic equilibrium of the deterministic system, we obtain the specific form of covariance matrix in the probability density around the quasi-positive equilibrium of the stochastic system. In addition, we also establish sufficient criteria for wiping out of the disease. Finally, several numerical simulations are performed to illustrate our theoretical conclusions.