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# Dynamics of Partial Differential Equations

## Volume 14 (2017)

### Number 2

### Stability and uniqueness of traveling waves of a non-local dispersal SIR epidemic model

Pages: 87 – 123

DOI: http://dx.doi.org/10.4310/DPDE.2017.v14.n2.a1

#### Authors

#### Abstract

This paper is mainly concerned with the exponential stability and uniqueness of traveling waves of a delayed nonlocal dispersal SIR epidemic model. We first prove the stability of traveling waves by using the weighted energy method, where the traveling waves are allowed to be non-monotone. Next we establish the exact asymptotic behavior of traveling waves at $- \infty$ by using Ikehara’s theorem. Then the uniqueness of traveling waves is obtained by the stability result. Finally, we discuss how the non-local dispersal affects the stability of traveling waves. The conclusion shows that the non-local dispersal slows down the convergence rate of the solution to the traveling waves.

#### Keywords

weighted energy method, traveling waves, exponential stability and uniqueness, nonlocal dispersal, the convergence rate

#### 2010 Mathematics Subject Classification

Primary 37-xx, 70-xx, 76-xx, 92-xx. Secondary 34-xx, 35-xx, 80-xx, 82-xx.

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