Abstract
In this paper, we investigate the global threshold-type result and traveling waves for a general HIV infection model involving CD\(4^+\) T cell death caused by caspase-1-mediated pyroptosis of the predominance. We first give the well-posedness of the model and establish the existence of a global attractor. In a bounded domain, the basic reproduction number, denoted by \(\Re _0\), is identified as a threshold parameter for indicating whether the infection occurs or not. Specifically, if \(\Re _0<1\), then the system admits a globally asymptotically stable infection-free steady state; if \(\Re _0>1\), the system is uniformly persistent. In an unbounded domain and homogeneous environment, we find that if \(\Re _0>1\) and wave speed is large enough, the system admits traveling wave solutions.
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Acknowledgements
The authors would like to thank the editor and anonymous reviewers for their valuable comments which led to a significant improvement of this study. The research was supported by the National Natural Science Foundation of China (Nos. 12071115, 12101309), the Heilongjiang Natural Science Funds for Distinguished Young Scholar (No. JQ2023A005), the Fundamental Research Funds for the Colleges and Universities in Heilongjiang Province (No. 2022-KYYWF-1113), and the Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems.
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Zhang, R., Xu, J. & Wang, J. Qualitative Analysis for an HIV Infection Model with Caspase-1-Mediated Pyroptosis of the Predominance: Threshold Dynamics and Traveling Waves. Qual. Theory Dyn. Syst. 22, 131 (2023). https://doi.org/10.1007/s12346-023-00828-6
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DOI: https://doi.org/10.1007/s12346-023-00828-6
Keywords
- Threshold dynamics
- Spatial heterogeneity
- Bounded domain
- Basic reproduction number
- Traveling wave solutions