Traveling waves for a nonlocal dispersal vaccination model with general incidence

Jinling Zhou, Yu Yang, Cheng Hsiung Hsu

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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 languageEnglish
Pages (from-to)1469-1495
Number of pages27
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume25
Issue number4
DOIs
StatePublished - 2020

Keywords

  • General incidence
  • Nonlocal dispersal
  • Schauder’s fixed point theorem
  • Traveling wave solutions
  • Two-sided Laplace transform
  • Vaccination

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