Traveling waves in a nonlocal dispersal Kermack-McKendrickepidemic model

Fei-Ying Yang; Yan Li; Wan-Tong Li; Zhi-Cheng Wang

doi:10.3934/dcdsb.2013.18.1969

Article Contents

2013, Volume 18, Issue 7: 1969-1993. Doi: 10.3934/dcdsb.2013.18.1969

This issue Previous Article Mean-field backward stochastic Volterra integral equations Next Article An erratum note on the paper: Positive periodic solution for Brillouin electron beam focusing system

Traveling waves in a nonlocal dispersal Kermack-McKendrick epidemic model

1.
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000
2.
School of Mathematic and Statistics, Lanzhou University, Lanzhou, Gansu 730000

Received: February 29, 2012

Revised: February 28, 2013

Published: August 2013

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Abstract

In this paper, we consider a Kermack-McKendrick epidemic model with nonlocal dispersal. We find that the existence and nonexistence of traveling wave solutions are determined by the reproduction number. To prove the existence of nontrivial traveling wave solutions, we construct an invariant cone in a bounded domain with initial functions being defined on, and apply Schauder's fixed point theorem as well as limiting argument. Here, the compactness of the support set of dispersal kernel is needed when passing to an unbounded domain in the proof. Moreover, the nonexistence of traveling wave solutions is obtained by Laplace transform if the speed is less than the critical velocity.

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Mathematics Subject Classification: 35K57, 37C65, 92D30.

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