Stationary distribution and ergodicity of an SEIR stochastic dengue epidemic model

The paper proposes an SEIR dengue epidemic model with a saturated incidence rate and establishes the corresponding stochastic model. The dynamical behavior of the stochastic system is investigated, which includes the existence and uniqueness of a global positive solution, the existence and uniqueness of an ergodic stationary distribution, and the sufficient conditions for extinction of the disease. Finally, numerical simulations are conducted to illustrate and support the effectiveness of certain theoretical results.