Dynamics of Partial Differential Equations
Volume 14 (2017)
Stability and uniqueness of traveling waves of a non-local dispersal SIR epidemic model
Pages: 87 – 123
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.
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.
Published 31 May 2017