Summary: In this paper, we further investigate the global dynamics of a stochastic differential equation SIS (susceptible-infected-susceptible) epidemic model recently proposed in [A. Gray et al., SIAM J. Appl. Math. 71, No. 3, 876–902 (2011; Zbl 1263.34068)]. We present a stochastic threshold theorem in term of a stochastic basic reproduction number \(R_0^S\): the disease dies out with probability one if \(R_0^S<1\), and the disease is recurrent if \(R_0^S\geqslant1\). We prove the existence and global asymptotic stability of a unique invariant density for the Fokker-Planck equation associated with the SDE SIS model when \(R_0^S > 1\). In term of the profile of the invariant density, we define a persistence basic reproduction number \(R_0^P\) and give a persistence threshold theorem: the disease dies out with large probability if \(R_0^P\leqslant1\), while persists with large probability if \(R_0^P>1\). Comparing the stochastic disease prevalence with the deterministic disease prevalence, we discover that the stochastic prevalence is bigger than the deterministic prevalence if the deterministic basic reproduction number \(R_0^D>2\). This shows that noise may increase severity of disease. Finally, we study the asymptotic dynamics of the stochastic SIS model as the noise vanishes and establish a sharp connection with the threshold dynamics of the deterministic SIS model in term of a limit stochastic threshold theorem.