On a Discretized SIS Epidemic Model with No Vertical Transmission

In this chapter, a discretized SIS epidemic model with no vertical transmission is presented and analysed. The examined model is the discrete version of a continuous model coming from the literature. We use only numerical schemes that produce systems of difference equations whose dynamics resembles of their continuous counterpart, i.e. the resulting discretized system is dynamically consistent with the original differential equation. Firstly, the basic properties of these discrete systems are discussed such as boundedness and positivity of solutions. Then possible equilibria are investigated regarding existence and stability.