Stability and Hopf bifurcation in a virus model with self-proliferation and delayed activation of immune cells
Stability and Hopf bifurcation in a virus model with self-proliferation and delayed activation of immune cells
复制标题
具有自我增殖和免疫细胞延迟激活的病毒模型中的稳定性和 Hopf 分岔
DOI：
10.3934/mbe.2020242
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发表时间：
2020
影响因子：
2.6
通讯作者：
Wang Kaifa
中科院分区：
文献类型：
--
作者：
Kong Huan;Zhang Guohong;Wang Kaifa
提出了一个新的数学模型，研究了病毒感染过程中免疫细胞的自增殖和延迟激活效应。通过构造适当的李雅普诺夫泛函，得到了边界平衡点的全局稳定性。对于正平衡点，以时滞为分支参数，得到了系统稳定和Hopf分支的条件。利用规范形理论和中心流形理论，得到了系统Hopf分支的方向和稳定性。这些结果表明，自增殖强度可以显着影响病毒感染的动力学，延迟激活的免疫细胞可以诱导周期性振荡的情况。随着延迟时间的增加，沿着增加，数值模拟给出了不同自扩散率下相应的分岔图，并验证了在一定条件下存在稳定切换现象。
A new mathematical model was proposed to study the effect of self-proliferation and delayed activation of immune cells in the process of virus infection. The global stability of the boundary equilibria was obtained by constructing appropriate Lyapunov functional. For positive equilibrium, the conditions of stability and Hopf bifurcation were obtained by taking the delay as the bifurcation parameter. Furthermore, the direction and stability of the Hopf bifurcation are derived by using the theory of normal form and center manifold. These results indicate that self-proliferation intensity can significantly affect the kinetics of viral infection, and the delayed activation of immune cells can induce periodic oscillation scenario. Along with the increase of delay time, numerical simulations give the corresponding bifurcation diagrams under different self-proliferation rates, and verify that there exists stability switch phenomenon under some conditions.