In this paper, we consider a stochastic SIS epidemic model with vaccination. We prove that the densities of the distributions of the solution can converge in L1 to an invariant density under appropriate conditions. Also we find the support of the invariant density.

In this paper, we discuss a multigroup SIR model with stochastic perturbation. We deduce the globally asymptotic stability of the disease-free equilibrium when R0≤1, which means the disease will die out. On the other hand, when R01, we derive the disease will prevail, which is measured through...