含延迟的病毒免疫系统动力学分析
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莆田学院 工程实训中心

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O175;R318.01?? ????????

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Dynamic Analysis of Virus Immune System with Time Delay
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Engineering Training Center, Putian University

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    摘要:

    目的 研究了一类病毒免疫模型在免疫强度和时间延迟影响下的动力学特性。方法 首先,通过理论推导确定了免疫强度的临界值,并利用数值模拟验证了病毒免疫系统在该临界点发生了鞍结分岔。其次,构建了含有时间延迟的病毒免疫系统模型,采用线性稳定性方法求解出平衡点,并根据特征根实部的符号来判断这些平衡点的稳定性。最后,研究时间延迟对动力学的影响。结果 含延迟系统的平衡点有鞍点、稳定结点、稳定焦点和不稳定结点,系统存在着双稳态现象。稳定焦点会随延迟的增大变成不稳定状态,出现Hopf分岔,由稳定收敛的平衡态变成周期性振荡状态,最终达到病毒爆发。不稳定结点的稳定性不受时间延迟影响,但随着延迟的增加,系统最终的趋向状态会发生变化。结论 研究的结果有助于深入理解病毒免疫系统的动力学机制,并为制定合理有效的治疗策略提供了理论依据。

    Abstract:

    Objective This paper studied the dynamical characteristics of a virus immune infection models under the influence of immune intensity and time delay. Methods First, we determined the critical value of immune intensity through theoretical derivation and used numerical simulations to verify that the virus immune system underwent saddle node bifurcation at this critical point. Second, we constructed a virus immune model with time delay, solved the equilibrium points using linear stability analysis, and determined the stability of these equilibrium points based on the sign of the real part of the characteristic roots. Finally, we studied the impact of time delay on dynamics. Results The equilibrium points of the system with delay include saddle, stable node, stable focus, and unstable node. It implied that system exhibited bistable phenomena. The stable focus became unstable as the delay increased, leading to Hopf bifurcations. The system transitioned from a stable convergent equilibrium to a periodic oscillatory state, ultimately resulting in a viral outbreak. The stability of unstable node is unaffected by time delay, but the system"s final convergence may have changed with increasing time delay. Conclusions The results of the study are helpful to further understand dynamic mechanisms of virus immune infection system, and provide a theoretical basis for formulating reasonable and effective treatment strategies.

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  • 收稿日期:2025-01-14
  • 最后修改日期:2025-03-10
  • 录用日期:2025-03-11
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