Resumen de Qualitative Analysis for an HIV Infection Model with Caspase-1-Mediated Pyroptosis of the Predominance: Threshold Dynamics and Traveling Waves
Ran Zhang, Jiangxue Xu, Jinliang Wang
In this paper, we investigate the global threshold-type result and traveling waves for a general HIV infection model involving CD4+ 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 0, is identified as a threshold parameter for indicating whether the infection occurs or not. Specifically, if 0 < 1, then the system admits a globally asymptotically stable infection-free steady state; if 0 > 1, the system is uniformly persistent. In an unbounded domain and homogeneous environment, we find that if 0 > 1 and wave speed is large enough, the system admits traveling wave solutions.
