Open AccessStability and Hopf bifurcation in a virus model with self-proliferation and delayed activation of immune cells
Author(s) -
Huan Kong,
Guo Hong Zhang,
Kai Fa Wang
Publication year - 2020
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2020242
Subject(s) - hopf bifurcation , center manifold , mathematics , bifurcation , saddle node bifurcation , stability (learning theory) , bifurcation diagram , transcritical bifurcation , control theory (sociology) , mathematical analysis , stability theory , oscillation (cell signaling) , lyapunov function , physics , chemistry , computer science , nonlinear system , quantum mechanics , biochemistry , control (management) , machine learning , artificial intelligence
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.