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Abstract
This paper is concerned with the existence and asymptotic behavior of traveling wave solutions for a nonlocal dispersal vaccination model with general incidence. We first apply the Schauder’s fixed point theorem to prove the existence of traveling wave solutions when the wave speed is greater than a critical speed c∗. Then we investigate the boundary asymptotic behaviour of traveling wave solutions at +∞ by using an appropriate Lyapunov function. Applying the method of two-sided Laplace transform, we further prove the non-existence of traveling wave solutions when the wave speed is smaller than c∗. From our work, one can see that the diffusion rate and nonlocal dispersal distance of the infected individuals can increase the critical speed c∗, while vaccination reduces the critical speed c∗. In addition, two specific examples are provided to verify the validity of our theoretical results, which cover and improve some known results.
Original language | English |
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Pages (from-to) | 1469-1495 |
Number of pages | 27 |
Journal | Discrete and Continuous Dynamical Systems - Series B |
Volume | 25 |
Issue number | 4 |
DOIs | |
State | Published - 2020 |
Keywords
- General incidence
- Nonlocal dispersal
- Schauder’s fixed point theorem
- Traveling wave solutions
- Two-sided Laplace transform
- Vaccination
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Dive into the research topics of 'Traveling waves for a nonlocal dispersal vaccination model with general incidence'. Together they form a unique fingerprint.Projects
- 1 Finished
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Interaction and Stability of Traveling Waves for Lattice Dynamical System and Reaction-Diffusion Equations(2/3)
1/08/19 → 31/07/20
Project: Research