Stability and Hopf bifurcation in a virus model with self-proliferation and delayed activation of immune cells
Autor: | Huan Kong, Guo Hong Zhang, Kai Fa Wang |
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Jazyk: | angličtina |
Rok vydání: | 2020 |
Předmět: |
Boundary (topology)
02 engineering and technology Viral infection Stability (probability) Models Biological Virus Quantitative Biology::Cell Behavior symbols.namesake Immune system 0502 economics and business 0202 electrical engineering electronic engineering information engineering QA1-939 Humans Computer Simulation Bifurcation Cell Proliferation Hopf bifurcation Physics Applied Mathematics 05 social sciences Mathematical analysis General Medicine delayed activation of immune cells Models Theoretical global stability Computational Mathematics stability switch Virus Diseases Modeling and Simulation self-proliferation symbols 020201 artificial intelligence & image processing viral infection General Agricultural and Biological Sciences hopf bifurcation 050203 business & management Center manifold TP248.13-248.65 Mathematics Biotechnology |
Zdroj: | Mathematical Biosciences and Engineering, Vol 17, Iss 5, Pp 4384-4405 (2020) |
ISSN: | 1551-0018 |
Popis: | 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. |
Databáze: | OpenAIRE |
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