In this research, we propose a stochastic multi-strain susceptible-exposed-infectious- recovered (SEIR) epidemic model with vaccination. A Kalman filter model will be applied for this present analysis. We will construct an EM algorithm to estimate the parameters. Additionally, we will evaluate its predictive effect for the number of infected patients, and will discuss the possibility of epidemic control under the different immune effects of the vaccine against multiple strains. Further research efforts and implications are discussed.