Abstract: This paper deals with the existence, non-existence and asymptotic behaviors of traveling wave solutions to a class of cholera epidemic system with spatio-temporal delay and nonlocal dispersal. By constructing the upper and lower solutions, the existence of traveling waves to the system is converted into the fixed point problem of a nonlinear operator on a closed and convex cone, and thus the existence, boundedness and asymptotic behavior at negative infinity of traveling waves of the system are proved by applying Schauder's fixed point theorem, limit theory and analysis techniques. In addition, the nonexistence of traveling waves of the system is also established based on the two-sided Laplace transform and the method of proof by contradiction.

Key words: nonlocal dispersal, spatio-temporal delay, traveling wave solutions