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 PDF

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

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.

References

J. R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency, J. Animal Ecol. 44 (1975), 331–340.
D. L. DeAngelis, R. A. Goldstein, and R. V. O’Neill, A model for trophic interaction, Ecology 56 (1975), 881–892.
Changbing Hu, Yang Kuang, Bingtuan Li, and Hao Liu, Spreading speeds and traveling wave solutions in cooperative integral-differential systems, Discrete Contin. Dyn. Syst. Ser. B 20 (2015), no. 6, 1663–1684. MR 3356550, DOI 10.3934/dcdsb.2015.20.1663
Gang Huang, Wanbiao Ma, and Yasuhiro Takeuchi, Global properties for virus dynamics model with Beddington-DeAngelis functional response, Appl. Math. Lett. 22 (2009), no. 11, 1690–1693. MR 2569065, DOI 10.1016/j.aml.2009.06.004
Yu Jin and Xiao-Qiang Zhao, Spatial dynamics of a nonlocal periodic reaction-diffusion model with stage structure, SIAM J. Math. Anal. 40 (2009), no. 6, 2496–2516. MR 2481304, DOI 10.1137/070709761
Xiulan Lai and Xingfu Zou, Modeling cell-to-cell spread of HIV-1 with logistic target cell growth, J. Math. Anal. Appl. 426 (2015), no. 1, 563–584. MR 3306388, DOI 10.1016/j.jmaa.2014.10.086
Yan Li, Wan-Tong Li, and Fei-Ying Yang, Traveling waves for a nonlocal dispersal SIR model with delay and external supplies, Appl. Math. Comput. 247 (2014), 723–740. MR 3270878, DOI 10.1016/j.amc.2014.09.072
Xing Liang and Xiao-Qiang Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure Appl. Math. 60 (2007), no. 1, 1–40. MR 2270161, DOI 10.1002/cpa.20154
Xing Liang and Xiao-Qiang Zhao, Spreading speeds and traveling waves for abstract monostable evolution systems, J. Funct. Anal. 259 (2010), no. 4, 857–903. MR 2652175, DOI 10.1016/j.jfa.2010.04.018
Lili Liu, Rui Xu, and Zhen Jin, Global dynamics of a spatial heterogeneous viral infection model with intracellular delay and nonlocal diffusion, Appl. Math. Model. 82 (2020), 150–167. MR 4065738, DOI 10.1016/j.apm.2020.01.035
C. Connell McCluskey and Yu Yang, Global stability of a diffusive virus dynamics model with general incidence function and time delay, Nonlinear Anal. Real World Appl. 25 (2015), 64–78. MR 3351011, DOI 10.1016/j.nonrwa.2015.03.002
Shao-Xia Qiao, Fei-Ying Yang, and Wan-Tong Li, Traveling waves of a nonlocal dispersal SEIR model with standard incidence, Nonlinear Anal. Real World Appl. 49 (2019), 196–216. MR 3934070, DOI 10.1016/j.nonrwa.2019.03.003
Wei Wang and Wanbiao Ma, Travelling wave solutions for a nonlocal dispersal HIV infection dynamical model, J. Math. Anal. Appl. 457 (2018), no. 1, 868–889. MR 3702734, DOI 10.1016/j.jmaa.2017.08.024
Wei Wang and Wanbiao Ma, A diffusive HIV infection model with nonlocal delayed transmission, Appl. Math. Lett. 75 (2018), 96–101. MR 3692166, DOI 10.1016/j.aml.2017.06.010
Wei Wang, Wanbiao Ma, and Xiulan Lai, Repulsion effect on superinfecting virions by infected cells for virus infection dynamic model with absorption effect and chemotaxis, Nonlinear Anal. Real World Appl. 33 (2017), 253–283. MR 3543122, DOI 10.1016/j.nonrwa.2016.04.013
David Vernon Widder, The Laplace Transform, Princeton Mathematical Series, vol. 6, Princeton University Press, Princeton, N. J., 1941. MR 0005923
Yiyi Zhang and Zhiting Xu, Dynamics of a diffusive HBV model with delayed Beddington-DeAngelis response, Nonlinear Anal. Real World Appl. 15 (2014), 118–139. MR 3110559, DOI 10.1016/j.nonrwa.2013.06.005
Guangyu Zhao and Shigui Ruan, Spatial and temporal dynamics of a nonlocal viral infection model, SIAM J. Appl. Math. 78 (2018), no. 4, 1954–1980. MR 3828867, DOI 10.1137/17M1144106
Wen-Bing Xu, Wan-Tong Li, and Guo Lin, Nonlocal dispersal cooperative systems: acceleration propagation among species, J. Differential Equations 268 (2020), no. 3, 1081–1105. MR 4029000, DOI 10.1016/j.jde.2019.08.039