Stationary distribution and probability density function of a stochastic COVID-19 infections model with general incidence

With the sudden outbreak of COVID-19 all over the world, vaccination was one of the most effective treatments. In this paper, a stochastic COVID-19 model with vaccination is developed. We first prove that the stochastic model has a unique global solution by constructing the corresponding Lyapunov function. Then, sufficient condition for ergodic stationary distribution v(& sdot;) is provided under the condition R-o(s) > 1 . Moreover, by applying the six-dimensional Fokker- Planck equation, we obtain the explicit expression of the probability density function near quasi-local equilibrium Q(& lowast;), which has the form of lognormal density function. Finally, numerical simulations are presented to verify the above conclusions.