  This paper deals with a simplified SIS model, which describes the
transmission of the disease in time-periodic heterogeneous environment. To
understand the impact of spatial heterogeneity of environment and small
advection on the persistence and eradication of an infectious disease, the left
and right free boundaries are introduced to represent the expanding fronts. The
basic reproduction numbers $R_0^D$ and $R_0^F(t)$, which depends on spatial
heterogeneity, temporal periodicity and advection, are introduced. A
spreading-vanishing dichotomy is established and sufficient conditions for the
spreading and vanishing of the disease are given. The asymptotic spreading
speeds for the left and right fronts are also presented.
