Multigroup SIR epidemic model with stochastic perturbation

► We study the dynamical behavior of a stochastic multigroup SIR model. ► We deduce the globally asymptotic stability of the disease-free equilibrium when R0≤1. ► When R0>1, we prove the system is persistent in the mean to show the disease will prevail. ► We mainly use the Lyapunov function and graph theory to prove our results.