## Abstract

This paper is concerned with propagation dynamics in a nonlocal dispersal HIV infection model. The existence and asymptotic behavior of traveling waves with wave speeds not less than a critical speed were derived in the recent work of Wang and Ma [J. Math. Anal. Appl. 457 (2018), pp. 868–889]. However, the asymptotic behavior of the critical traveling wave and minimum wave speed were not clarified completely. In this article, we first affirm the asymptotic behavior of the critical traveling wave at negative infinity. Then we prove the non-existence of traveling waves when either the basic reproduction number R_{0} < 1 or the wave speed is less than the critical spreed and R_{0} > 1. Our result provides a complete complement for the wave propagation in the infection model.

Original language | English |
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Pages (from-to) | 4867-4877 |

Number of pages | 11 |

Journal | Proceedings of the American Mathematical Society |

Volume | 150 |

Issue number | 11 |

DOIs | |

State | Published - 1 Nov 2022 |

## Keywords

- Basic reproduction number
- HIV infection model
- Nonlocal dispersal
- Traveling wave
- Two-sided Laplace transform