Discrete-time SIS models

I will talk about discrete-time SIS models which were based on their continuous counterparts. The first type of models reflects the dynamics of epidemics in a homogeneous population - in this case two-dimensional systems are used. The second type of models corresponds to dynamics in a heterogeneous population - for this issue we will consider four-dimensional systems which are based on the two-dimensional ones. In order to discretize the continuous systems, explicit Euler scheme and non-standard discretization method were used. I will present the basic properties of the systems. In particular, the stability analysis will be discussed.