  In this article, we construct a numerical method for a stochastic version of
the Susceptible Infected Susceptible (SIS) epidemic model, expressed by a
suitable stochastic differential equation (SDE), by using the semi-discrete
method to a suitable transformed process. We prove the strong convergence of
the proposed method, with order $1,$ and examine its stability properties.
Since SDEs generally lack analytical solutions, numerical techniques are
commonly employed. Hence, the research will seek numerical solutions for
existing stochastic models by constructing suitable numerical schemes and
comparing them with other schemes. The objective is to achieve a qualitative
and efficient approach to solving the equations. Additionally, for models that
have not yet been proposed for stochastic modeling using SDEs, the research
will formulate them appropriately, conduct theoretical analysis of the model
properties, and subsequently solve the corresponding SDEs.

Numerical Analysis;Numerical Analysis;Probability