Dynamics of a Stochastic Viral Infection Model with Immune Response

2017 ◽  
Vol 12 (5) ◽  
pp. 15-32 ◽  
Author(s):  
M. Mahrouf ◽  
K. Hattaf ◽  
N. Yousfi
Keyword(s):  
Immune Response ◽  
Viral Infection ◽  
Infection Model ◽  
Viral Infection Model

Global Stability and Hopf Bifurcation in a Delayed Viral Infection Model with Cell-to-Cell Transmission and Humoral Immune Response

2019 ◽  
Vol 29 (12) ◽  
pp. 1950161 ◽  
Author(s):  
Jinhu Xu ◽  
Yan Geng ◽  
Suxia Zhang
Keyword(s):  
Immune Response ◽  
Hopf Bifurcation ◽  
Viral Infection ◽  
Humoral Immune Response ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Humoral Immune ◽  
Cell Transmission ◽  
Viral Infection Model ◽  
Intracellular Delays

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.

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

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.

scholarly journals Global stability of a distributed delayed viral model with general incidence rate

2018 ◽  
Vol 16 (1) ◽  
pp. 1374-1389
Author(s):  
Eric Ávila-Vales ◽  
Abraham Canul-Pech ◽  
Erika Rivero-Esquivel
Keyword(s):  
Immune Response ◽  
Viral Infection ◽  
Global Stability ◽  
Numerical Simulations ◽  
Incidence Rate ◽  
Existence And Uniqueness ◽  
Lyapunov Functional ◽  
Infection Model ◽  
General Incidence Rate ◽  
Viral Infection Model

AbstractIn this paper, we discussed a infinitely distributed delayed viral infection model with nonlinear immune response and general incidence rate. We proved the existence and uniqueness of the equilibria. By using the Lyapunov functional and LaSalle invariance principle, we obtained the conditions of global stabilities of the infection-free equilibrium, the immune-exhausted equilibrium and the endemic equilibrium. Numerical simulations are given to verify the analytical results.

scholarly journals Analysis of a viral infection model with delayed immune response

2010 ◽  
Vol 34 (9) ◽  
pp. 2388-2395 ◽  
Author(s):  
Qizhi Xie ◽  
Dongwei Huang ◽  
Shuangde Zhang ◽  
Jin Cao
Keyword(s):  
Immune Response ◽  
Viral Infection ◽  
Infection Model ◽  
Viral Infection Model

A viral infection model with periodic immune response and nonlinear CTL response

2010 ◽  
Vol 80 (12) ◽  
pp. 2309-2316 ◽  
Author(s):  
Yu Ji ◽  
Lequan Min ◽  
Yu Zheng ◽  
Yongmei Su
Keyword(s):  
Immune Response ◽  
Viral Infection ◽  
Infection Model ◽  
Ctl Response ◽  
Viral Infection Model

Viral infection model with periodic lytic immune response

2006 ◽  
Vol 28 (1) ◽  
pp. 90-99 ◽  
Author(s):  
Kaifa Wang ◽  
Wendi Wang ◽  
Xianning Liu
Keyword(s):  
Immune Response ◽  
Viral Infection ◽  
Infection Model ◽  
Viral Infection Model

scholarly journals Spatiotemporal Dynamics of a Generalized Viral Infection Model with Distributed Delays and CTL Immune Response

Computation ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 21 ◽  
Author(s):  
Khalid Hattaf
Keyword(s):  
Immune Response ◽  
Viral Infection ◽  
Cytotoxic T Lymphocyte ◽  
Distributed Delays ◽  
Infection Model ◽  
Cell Infection ◽  
Incidence Functions ◽  
Dynamics Models ◽  
Ctl Immune Response ◽  
Viral Infection Model

In this paper, we propose and investigate a diffusive viral infection model with distributed delays and cytotoxic T lymphocyte (CTL) immune response. Also, both routes of infection that are virus-to-cell infection and cell-to-cell transmission are modeled by two general nonlinear incidence functions. The well-posedness of the proposed model is also proved by establishing the global existence, uniqueness, nonnegativity and boundedness of solutions. Moreover, the threshold parameters and the global asymptotic stability of equilibria are obtained. Furthermore, diffusive and delayed virus dynamics models presented in many previous studies are improved and generalized.

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