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
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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