中文摘要：

This paper is concerned with traveling wave solutions to a nonlocal dispersal epidemic model.Combining the upper and lower solutions and monotone iteration method,we establish the existence of nondecreasing traveling wave fronts for the speed being larger than the critical one.Furthermore,by the approximation method,the existence of traveUng wave fronts for the critical speed is estabUshed as weU.Finally,we discuss the nonexistence of traveling wave fronts for the speed being smaller than critical one by Laplace transform.

英文摘要：

This paper is concerned with traveling wave solutions to a nonlocal dispersal epide- mic model. Combining the upper and lower solutions and monotone iteration method, we establish the existence of nondecreasing traveling wave fronts for the speed being larger than the critical one. Furthermore, by the approximation method, the existence of traveling wave fronts for the critical speed is established as well. Finally, we discuss the nonexistence of traveling wave fronts for the speed being smaller than critical one by Laplace transform.