Dynamic Properties for a Second-Order Stochastic SEIR Model with Infectivity in Incubation Period and Homestead-Isolation of the Susceptible Population

In this article, we analyze a second-order stochastic SEIR epidemic model with latent infectious and susceptible populations isolated at home. Firstly, by putting forward novel inequality, provide criterion for the presence of an ergodic stationary distribution model. Secondly, establish sufficient conditions extinction. Thirdly, solving corresponding Fokker–Plank equation, derive probability density function around quasi-endemic equilibrium Finally, using data deterministic model, two numerical tests are presented to illustrate validity theoretical results. Our conclusions demonstrate that nations should persevere in their quarantine policies curb viral transmission when COVID-19 pandemic proceeds spread internationally.