Characterization of dynamics of a generalized mosquito-borne disease model with Ornstein-Uhlenbeck process

In this paper, a mosquito-borne disease model with general incidence rate is presented and its transmission dynamics are studied. Firstly, locally asymptotic stability of the disease-free equilibrium point and global stability of endemic equilibrium point are analyzed. On the other hand, considering the transmission of the infectious disease is inevitably affected by environmental noise, a stochastic model with Ornstein-Uhlenbeck process is adopted to study the transmission dynamics of mosquito-borne disease model. Specifically, sufficient conditions for the existence of stationary distribution and exponential extinction are established by constructing a series of suitable Lyapunov functions. In addition, the probability density function corresponding to the stationary distribution near the quasi-equilibrium is also investigated. Finally, several numerical simulations are performed to verify the theoretical results and investigate the influence of stochastic perturbations on the model.