Traveling waves of a nonlocal dispersal SEIR model with standard incidence. (English) Zbl 1429.92135
Summary: This paper is devoted to investigating the traveling wave solutions of a nonlocal dispersal SEIR epidemic model with standard incidence. We find that the existence and nonexistence of traveling wave solutions are determined by the basic reproduction number and the critical wave speed. Through considering a truncate problem, combining with Schauder’s fixed-point theorem and applying a limiting argument, we prove the existence of traveling wave solutions. Meanwhile, the nonexistence of traveling wave solutions is showed by the Laplace transform method. Furthermore, the existence of traveling wave solutions with critical wave speed is also established by a delicate analysis. We also point out that both the nonlocal dispersal and coupling of system in the model bring some difficulties in the study of traveling wave solutions.
MSC:
| 92D30 | Epidemiology |
| 35C07 | Traveling wave solutions |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
Keywords:
nonlocal dispersal; Schauder’s fixed-point theorem; traveling wave solutions; critical wave speedReferences:
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