A HIV‐1 Dynamic Model With Degenerate Diffusion, Time Delay and Immune Impairment
Li Yang, Yantao Luo, Tingting Zheng, Zhidong Teng
Source abstract
ABSTRACT Considering the coupled effects of multiple key biological mechanisms, including diffusion effects, the time delay in viral maturation and immune impairment, we innovatively propose a highly comprehensive reaction–diffusion dynamics model for HIV‐1 infection. First, we analyze the well‐posedness for the model, including the global existence, uniqueness, non‐negativity, and boundedness of solutions. Second, we compute the immune‐unactivated reproduction number and the immune‐activated reproduction number . By employing Lyapunov functionals and LaSalle's invariance principle, we prove the global threshold dynamics of the model. Furthermore, we demonstrate that when , the system admits no traveling wave solutions connecting the infection‐free equilibrium to itself. Finally, numerical simulations not only validate these theoretical results but also reveal that the virus‐to‐cell transmission route exhibits higher sensitivity in influencing , while reducing the immune impairment rate significantly enhances the intensity of the CTL response. This study provides a unified theoretical framework for understanding HIV‐1 infection dynamics under complex biological factors and offers mathematical insights for optimizing combination therapeutic strategies.
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