Abstract
Since November 2019, each country in the world has been affected by COVID-19, which has claimed more than four million lives. As an infectious disease, COVID-19 has a stronger transmission power and faster propagation speed. In fact, environmental noise is an inevitable important factor in the real world. This paper mainly gives a new random infectious disease system under infection rate environmental noise. We give the existence and uniqueness of the solution of the system and discuss the ergodic stationary distribution and the extinction conditions of the system. The probability density function of the stochastic system is studied. Some digital simulations are used to demonstrate the probability density function and the extinction of the system.