A Discrete SIS Model of Epidemic for Heterogeneous Population without Discretization of its Continuous Counterpart

We propose a model of an infectious disease transmission in a heterogeneous population consisting of two different subpopulations: individuals with low and high susceptibility to an infection. This is a discrete model which was built without discretization of its continuous counterpart.
We investigate conditions for existence and local stability of stationary states.
We compute the basic reproduction number R0 of the given system, which determines the local stability of the disease-free stationary state.
Additionally, we consider a situation when there is no illness transmission in the subpopulation with the low susceptibility.
Theoretical results are complemented with numerical simulations.