In this paper, we study the asymptotic and stability dynamics of a chemotaxis model in volume filling constraints on HIV-1-incorporating cytotoxic T lymphocytes (CTLs) cells in defense mechanism against the virus infection. The system of uninfected \(\hbox {CD}4^{+}\hbox {T}\)-cells, infected and CTL defense cells is globally well-defined in \(\Omega \times (0,\infty )\), with uninfected \(\hbox {CD}4^{+}\hbox {T}\) and CTL cells remaining bounded, while the HIV-1-activated cells decay to the null state at time \(t=\infty \). Routh–Hurwitz criteria yields asymptotical stability of the system, if the CTL threshold value is sufficiently large with CTL decay small, and instability otherwise. In control theory, it is implied that a bounded control yields the system not completely controllable, but bounded input-bounded output stable (b.i.b.o.-stable) with stabilizability and detectability not guaranteed. If guaranteed, the system is asymptotically stable if and only if it is b.i.b.o.-stable. In addition, numerical simulation results of the model are provided.

中文翻译：

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HIV-1-细胞毒性T淋巴细胞（CTL）趋化模型的渐近和稳定性动力学。

在本文中，我们研究了趋化性模型的渐进性和稳定性动力学，该模型在掺入HIV-1的细胞毒性T淋巴细胞（CTLs）细胞抵御病毒感染的防御机制中的体积填充约束中。未感染\（\ hbox {CD} 4 ^ {+} \ hbox {T} \）-细胞，感染和CTL防御细胞的系统在\（\ Omega \ times（0，\ infty）\ ），未感染的\（\ hbox {CD} 4 ^ {+} \ hbox {T} \）和CTL细胞仍然处于受限制状态，而HIV-1激活的细胞在时间\（t = \ infty \）。如果CTL阈值足够大而CTL衰减很小，则Routh–Hurwitz准则会产生系统的渐近稳定性，否则，不稳定。在控制理论中，这暗示着有界控制会导致系统不完全可控，但有界输入有界输出稳定（双向稳定），无法保证稳定性和可检测性。如果有保证，则系统仅在Bibo稳定的情况下才是渐近稳定的。另外，提供了模型的数值模拟结果。