Liu Chunhua, Kong Lei
School of Mathematics and Statistics, Yangtze Normal University, Fuling district, 408100 Chongqing city, P.R. China.
School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guizhou, 550025 P.R. China.
Adv Differ Equ. 2020;2020(1):581. doi: 10.1186/s13662-020-03035-8. Epub 2020 Oct 17.
We consider a four-dimensional HIV model that includes healthy cells, infected cells, primary cytotoxic T-lymphocyte response (CTLp), and secondary cytotoxic T-lymphocyte response (CTLe). The CTL memory generation depends on CD4 T-cell help, and infection of CD4 T cells results in impaired T-cell help. We show that the system has up to five equilibria. By the Routh-Hurwitz theorem and central manifold theorem we obtain some sufficient conditions for the local stability, globally stability of the equilibria, and the bifurcations. We still discover the bistability case where in the system there may coexist two stable equilibria or a stable equilibrium together with a stable limit cycle. Several numerical analyses are carried out to illustrate the validity of our theoretical results.
我们考虑一个四维的HIV模型，该模型包括健康细胞、被感染细胞、初级细胞毒性T淋巴细胞反应（CTLp）和次级细胞毒性T淋巴细胞反应（CTLe）。CTL记忆的产生依赖于CD4 T细胞的辅助，而CD4 T细胞的感染会导致T细胞辅助功能受损。我们证明该系统最多有五个平衡点。通过劳斯-赫尔维茨定理和中心流形定理，我们得到了关于平衡点的局部稳定性、全局稳定性以及分岔的一些充分条件。我们还发现了双稳情况，即系统中可能共存两个稳定平衡点，或者一个稳定平衡点与一个稳定极限环共存。进行了若干数值分析以说明我们理论结果的有效性。
