Dynamics of an HIV model with cytotoxic T-lymphocyte memory

Advances in Difference Equations

Lei Kong¹  Chunhua Liu² 

[1] School of Mathematics and Statistics, Guizhou University of Finance and Economics, 550025, Guizhou, P.R. China;School of Mathematics and Statistics, Yangtze Normal University, Fuling district, 408100, Chongqing city, P.R. China;

关键词: HIV model;    Routh–Hurwitz theorem;    Central manifold;    Bistability;    Hopf bifurcation;   

DOI  :  10.1186/s13662-020-03035-8

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY