Hopf bifurcation analysis of a delayed viral infection model in computer networks

We have developed a class of viral infection model with cell-to-cell transmission and humoral immune response. The model addresses both immune and intracellular delays. We also constructed Lyapunov functionals to establish the global dynamical properties of the equilibria. Theoretical results indicate that considering only two intracellular delays did not affect the dynamical behavior of the model, but incorporating an immune delay greatly affects the dynamics, i.e. an immune delay may destabilize the immunity-activated equilibrium and lead to Hopf bifurcation, oscillations and stability switches. Our results imply that an immune delay dominates the intracellular delays in the model. We also investigated the direction of the Hopf bifurcation and the stability of the periodic solutions by applying normal form and center manifold theory, and investigated the existence of global Hopf bifurcation by regarding the immune delay as a bifurcation parameter. Numerical simulations are carried out to support the analytical conclusions.

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EFFECT OF TIME DELAY ON SPATIAL PATTERNS IN A AIRAL INFECTION MODEL WITH DIFFUSION

Mathematical Modelling and Analysis ◽

10.3846/13926292.2016.1137503 ◽

2016 ◽

Vol 21 (2) ◽

pp. 143-158

Author(s):

Jia Liu ◽

Qunying Zhang ◽

Canrong Tian

Keyword(s):

Immune Response ◽

Hopf Bifurcation ◽

Time Delay ◽

Viral Infection ◽

Spatial Patterns ◽

Infection Model ◽

The Stability ◽

Manifold Theory ◽

Viral Infection Model ◽

Theoretical Results

This paper is concerned with the dynamics of a viral infection model with diffusion under the assumption that the immune response is retarded. A time delay is incorporated into the model described the delayed immune response after viral infection. Based upon a stability analysis, we demonstrate that the appearance, or the absence, of spatial patterns is determined by the delay under some conditions. Moreover, the spatial patterns occurs as a consequence of Hopf bifurcation. By applying the normal form and the center manifold theory, the direction as well as the stability of the Hopf bifurcation is explored. In addition, a series of numerical simulations are performed to illustrate our theoretical results.

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Stability and Hopf bifurcation for a viral infection model with delayed non-lytic immune response

Journal of Applied Mathematics and Computing ◽

10.1007/s12190-009-0285-y ◽

2009 ◽

Vol 33 (1-2) ◽

pp. 251-265 ◽

Cited By ~ 18

Author(s):

Xinyu Song ◽

Shaoli Wang ◽

Xueyong Zhou

Keyword(s):

Immune Response ◽

Hopf Bifurcation ◽

Viral Infection ◽

Infection Model ◽

Viral Infection Model

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Stability and Hopf bifurcation in a delayed viral infection model with mitosis transmission

Applied Mathematics and Computation ◽

10.1016/j.amc.2015.02.053 ◽

2015 ◽

Vol 259 ◽

pp. 293-312 ◽

Cited By ~ 6

Author(s):

Eric Avila-Vales ◽

Noé Chan-Chí ◽

Gerardo E. García-Almeida ◽

Cruz Vargas-De-León

Keyword(s):

Hopf Bifurcation ◽

Viral Infection ◽

Infection Model ◽

Viral Infection Model

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Stability and bifurcation analysis for a delayed viral infection model with full logistic proliferation

International Journal of Biomathematics ◽

10.1142/s1793524520500333 ◽

2020 ◽

Vol 13 (05) ◽

pp. 2050033

Author(s):

Yan Geng ◽

Jinhu Xu

Keyword(s):

Hopf Bifurcation ◽

Viral Infection ◽

Time Delays ◽

Infection Model ◽

Lyapunov Functionals ◽

Stability Switches ◽

Two Delays ◽

Infected Cells ◽

Bifurcation And Stability ◽

Viral Infection Model

In this paper, we study a delayed viral infection model with cellular infection and full logistic proliferations for both healthy and infected cells. The global asymptotic stabilities of the equilibria are studied by constructing Lyapunov functionals. Moreover, we investigated the existence of Hopf bifurcation at the infected equilibrium by regarding the possible combination of the two delays as bifurcation parameters. The results show that time delays may destabilize the infected equilibrium and lead to Hopf bifurcation. Finally, numerical simulations are carried out to illustrate the main results and explore the dynamics including Hopf bifurcation and stability switches.

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