Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
Volume 18, Issue 7, Pages 1969-1993Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdsb.2013.18.1969
Keywords
Kermack-McKendrick; traveling waves; nonlocal dispersal; Schauder's fixed point theorem; Laplace transform
Categories
Funding
- NSF of China [11031003, 11271172, 11071105]
- Program for New Century Excellent Talents in University [NCET-10-0470]
- Fundamental Research Funds for the Central Universities [lzujbky-2011-k27]
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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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