Stability analysis for delayed viral infection model with multitarget cells and general incidence rate

2015 ◽  
Vol 09 (01) ◽  
pp. 1650007 ◽  
Author(s):  
Jinliang Wang ◽  
Xinxin Tian ◽  
Xia Wang
Keyword(s):  
Viral Infection ◽  
Incidence Rate ◽  
Time Delays ◽  
Infection Model ◽  
Target Cells ◽  
Uniform Persistence ◽  
Nonlinear Incidence Rate ◽  
General Incidence Rate ◽  
Infected Cells ◽  
Viral Infection Model

In this paper, the sharp threshold properties of a (2n + 1)-dimensional delayed viral infection model are investigated. This model combines with n classes of uninfected target cells, n classes of infected cells and nonlinear incidence rate h(x, v). Two kinds of distributed time delays are incorporated into the model to describe the time needed for infection of uninfected target cells and virus replication. Under certain conditions, it is shown that the basic reproduction number is a threshold parameter for the existence of the equilibria, uniform persistence, as well as for global stability of the equilibria of the model.

scholarly journals Global dynamics for a class of infection-age model with nonlinear incidence

2018 ◽  
Vol 24 (1) ◽  
pp. 47-72 ◽  
Author(s):  
Yuji Li ◽  
Rui Xu ◽  
Jiazhe Lin
Keyword(s):  
Viral Infection ◽  
Reproduction Number ◽  
Infection Model ◽  
Uniform Persistence ◽  
Global Dynamics ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Infection Age ◽  
Age Model ◽  
Viral Infection Model

In this paper, we propose an HBV viral infection model with continuous age structure and nonlinear incidence rate. Asymptotic smoothness of the semi-flow generated by the model is studied. Then we caculate the basic reproduction number and prove that it is a sharp threshold determining whether the infection dies out or not. We give a rigorous mathematical analysis on uniform persistence by reformulating the system as a system of Volterra integral equations. The global dynamics of the model is established by using suitable Lyapunov functionals and LaSalle's invariance principle. We further investigate the global behaviors of the HBV viral infection model with saturation incidence through numerical simulations.

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.

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

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.

scholarly journals Stability Analysis for Viral Infection Model with Multitarget Cells, Beddington-DeAngelis Functional Response, and Humoral Immunity

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Xinxin Tian ◽  
Jinliang Wang
Keyword(s):  
Immune Response ◽  
Viral Infection ◽  
Incidence Rate ◽  
Functional Response ◽  
Humoral Immunity ◽  
Infection Model ◽  
Target Cells ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Viral Infection Model

We formulate a (2n+2)-dimensional viral infection model with humoral immunity,nclasses of uninfected target cells and  nclasses of infected cells. The incidence rate of infection is given by nonlinear incidence rate, Beddington-DeAngelis functional response. The model admits discrete time delays describing the time needed for infection of uninfected target cells and virus replication. By constructing suitable Lyapunov functionals, we establish that the global dynamics are determined by two sharp threshold parameters:R0andR1. Namely, a typical two-threshold scenario is shown. IfR0≤1, the infection-free equilibriumP0is globally asymptotically stable, and the viruses are cleared. IfR1≤1<R0, the immune-free equilibriumP1is globally asymptotically stable, and the infection becomes chronic but with no persistent antibody immune response. IfR1>1, the endemic equilibriumP2is globally asymptotically stable, and the infection is chronic with persistent antibody immune response.

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