  We investigate an epidemic model based on Bailey's continuous differential
system. In the continuous time domain, we extend the classical model to
time-dependent coefficients and present an alternative solution method to
Gleissner's approach. If the coefficients are constant, both solution methods
yield the same result. After a brief introduction to time scales, we formulate
the SIR (susceptible-infected-removed) model in the general time domain and
derive its solution. In the discrete case, this provides the solution to a new
discrete epidemic system, which exhibits the same behavior as the continuous
model. The last part is dedicated to the analysis of the limiting behavior of
susceptible, infected, and removed, which contains biological relevance.
