Abstract
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 υ(⋅) is provided under the condition R0s>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∗, which has the form of lognormal density function. Finally, numerical simulations are presented to verify the above conclusions.
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