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This paper focuses on the traveling waves for a nonlocal dispersal SIR model with renewal and spatio-temporal delay. By Schauder's fixed point theorem, the prior estimate, limit theory and analysis techniques, the existence and asymptotic behaviors of traveling waves are obtained, which essentially generalize the results of nonlocal SIR models without renewal and delay. Especially, it is difficult to establish the asymptotic behaviors of traveling waves for the appearance of spatio-temporal delay, which is overcome by some boundedness estimates and integral techniques for the generally nonlocal nonlinearity. Finally, the non-existence of traveling waves is also included.

Traveling waves for a nonlocal dispersal SIR model with renewal and spatio-temporal delay