A note on the propagation dynamics in a nonlocal dispersal HIV infection model

Yang, Yu; Hsu, Cheng-Hsiung; Zou, Lan; Zhou, Jinling

doi:10.1090/proc/16036

A note on the propagation dynamics in a nonlocal dispersal HIV infection model
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by Yu Yang, Cheng-Hsiung Hsu, Lan Zou and Jinling Zhou

Proc. Amer. Math. Soc. 150 (2022), 4867-4877

DOI: https://doi.org/10.1090/proc/16036

Published electronically: June 16, 2022

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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 $\mathcal {R}_0<1$ or the wave speed is less than the critical spreed and $\mathcal {R}_0>1$. Our result provides a complete complement for the wave propagation in the infection model.

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