In this work, we generalize the dynamic model introduced in Bohner and Streipert (Pliska Stud. Math. 26:11—28, 2016, [5]) in the context of epidemiology. This model exhibits many similarities to the continuous susceptible-infected-susceptible model and is therefore of particular interest to formulate a generalization of a continuous model on time scales. In this work, we extend the results in Bohner and Streipert (Pliska Stud. Math. 26:11—28, 2016, [5]) for time-dependent coefficients rather than constant parameters and derive an explicit solution. We further discuss the stability of periodic solutions for the corresponding discrete model with periodic coefficients. We conclude the analysis of the SIS model by considering time-dependent vital dynamics and derive its explicit solution on a general time scale.