  We study the existence and nonexistence of traveling waves of general
diffusive Kermack-McKendrick SIR models with standard incidence where the total
population is not constant. The three classes, susceptible $S$, infected $I$
and removed $R$, are all involved in the traveling wave solutions. We show that
the minimum speed for the existence of traveling waves for this
three-dimensional non-monotonic system can be derived from its linearizaion at
the initial disease-free equilibrium. The proof in this paper is based on
Schauder fixed point theorem and Laplace transform and provides a promising
method to deal with high dimensional epidemic models.
