  This paper is concerned with the conditions of existence and nonexistence of
traveling wave solutions (TWS) for a class of discrete diffusive epidemic
models. We find that the existence of TWS is determined by the so-called basic
reproduction number and the critical wave speed: When the basic reproduction
number R0 greater than 1, there exists a critical wave speed c* > 0, such that
for each c >= c * the system admits a nontrivial TWS and for c < c* there
exists no nontrivial TWS for the system. In addition, the boundary asymptotic
behaviour of TWS is obtained by constructing a suitable Lyapunov functional and
employing Lebesgue dominated convergence theorem. Finally, we apply our results
to two discrete diffusive epidemic models to verify the existence and
nonexistence of TWS.
