Summary: This work considers a multi-group epidemic SIR models with vaccination. The fluctuation of the environment is taken into account by introducing both color noise and white noise to a compartmental model. Unlike existing results on stochastic multigroup models, which were not successful in finding the reproduction numbers and fully classify the longtime behaviors of the models, we will provide a formula for the reproduction number \(\mathcal{R}_0\) of our model and will show that the disease is persistent if \(\mathcal{R}_0>1\) while the disease will be eradicated if \(\mathcal{R}_0\leq 1\). We also provide the explicit formulae for \(\mathcal{R}_0\) in some special cases. The formulae will be useful to determine the herb immunity threshold of the disease, which can be used to make right and timely policy to control a disease.