  It is important to study the global behavior of solutions to systems of
ordinary differential equations describing the transmission dynamics of
infectious disease. In this paper, we present a different approach from the
Lyapunov function used in most of them. This approach is based on the
Poincar\'e compactification. We then apply the method to a SIR endemic model as
a test case, and discuss its effectiveness and the potential applications of
this approach. In addition, we refine the discussion of dynamics near the
equilibrium, derive the asymptotic behavior, and mention its relation to the
basic reproduction number.
