With the inevitable environmental perturbations and complex population
movements, the analysis of troublesome influenza is harder to proceed.
Studies about the epidemic mathematical models can not only forecast the
development trend of influenza, but also have a beneficial influence on
the protection of health and the economy. Motivated by this, a
stochastic influenza model incorporating human mobility and the
Ornstein-Uhlenbeck process is established in this paper. Based on the
existence of the unique global positive solution, we obtain sufficient
conditions for influenza extinction and persistence, which are related
to the basic reproduction number in the corresponding deterministic
model. Notably, the analytical expression of the probability density
function of stationary distribution near the quasi-endemic equilibrium
is obtained by solving the challenging Fokker--Planck equation. Finally,
numerical simulations are performed to support the theoretical
conclusions, and the effect of main parameters and environmental
perturbations on influenza transmission are also investigated.