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

Huan Kong; Guohong Zhang; Kaifa Wang; Huan Kong; Guohong Zhang; Kaifa Wang

doi:10.3934/mbe.2020242

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 4384-4405. doi: 10.3934/mbe.2020242

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Research article Special Issues

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

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received: 14 April 2020 Accepted: 08 June 2020 Published: 22 June 2020

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.

Keywords:

Citation: Huan Kong, Guohong Zhang, Kaifa Wang. Stability and Hopf bifurcation in a virus model with self-proliferation and delayed activation of immune cells[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 4384-4405. doi: 10.3934/mbe.2020242

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Abstract

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