AbstractIn this paper we introduce and analyze a discrete SIS epidemic model for a homogeneous population. As a discretization method the strictly positive scheme was chosen. The presented model is built from its continuous counterpart known from literature. We firstly present basic properties of the system. Later we discuss local stability of stationary states and global stability for the disease-free stationary state. The results for this state are expressed with the use of the basic reproduction number. The main conclusion from our work is that conditions for stability of the stationary states do not depend on the step size of the discretization method. This fact stays in contrary to other discrete models analyzed in our previous papers. Theoretical results are accomplished with numerical simulations.