Stability and Hopf bifurcation in a virus model with self-proliferation and delayed activation of immune cells

Mathematical Biosciences and Engineering

Huan Kong¹  Guohong Zhang¹  Kaifa Wang¹ 

[1] School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;

关键词: viral infection;    self-proliferation;    delayed activation of immune cells;    global stability;    hopf bifurcation;    stability switch;   

DOI  :  10.3934/mbe.2020242

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown