Global dynamics of a discrete viral infection model with time delay, virus-to-cell and cell-to-cell transmissions

2017 ◽  
Vol 23 (11) ◽  
pp. 1853-1868 ◽  
Author(s):  
Jinling Zhou ◽  
Yu Yang
Keyword(s):  
Time Delay ◽  
Viral Infection ◽  
Infection Model ◽  
Global Dynamics ◽  
Viral Infection Model

scholarly journals Global Dynamics of a Delayed Fractional-Order Viral Infection Model With Latently Infected Cells

2021 ◽  
Vol 7 ◽  
Author(s):  
C. Rajivganthi ◽  
F. A. Rihan
Keyword(s):  
Time Delay ◽  
Viral Infection ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Steady States ◽  
Infection Model ◽  
Global Dynamics ◽  
Local Asymptotic Stability ◽  
Latently Infected ◽  
Viral Infection Model

In this paper, we propose a fractional-order viral infection model, which includes latent infection, a Holling type II response function, and a time-delay representing viral production. Based on the characteristic equations for the model, certain sufficient conditions guarantee local asymptotic stability of infection-free and interior steady states. Whenever the time-delay crosses its critical value (threshold parameter), a Hopf bifurcation occurs. Furthermore, we use LaSalle’s invariance principle and Lyapunov functions to examine global stability for infection-free and interior steady states. Our results are illustrated by numerical simulations.

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.

Complete Global Dynamics of a Delayed Viral Infection Model with Lytic and Nonlytic Effectors

SeMA Journal ◽  
2012 ◽  
Vol 60 (1) ◽  
pp. 27-50 ◽  
Author(s):  
Yukihiko Nakata ◽  
Yoichi Enatsu ◽  
Yoshiaki Muroya
Keyword(s):  
Viral Infection ◽  
Infection Model ◽  
Global Dynamics ◽  
Viral Infection Model

Dynamical behaviors of a general humoral immunity viral infection model with distributed invasion and production

2017 ◽  
Vol 10 (03) ◽  
pp. 1750035 ◽  
Author(s):  
A. M. Ełaiw ◽  
N. H. AlShamrani ◽  
K. Hattaf
Keyword(s):  
Viral Infection ◽  
Humoral Immunity ◽  
Lyapunov Functions ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Global Dynamics ◽  
Nonlinear Mathematical Model ◽  
Dynamical Behaviors ◽  
Number Formula ◽  
Viral Infection Model

A general nonlinear mathematical model for the viral infection with humoral immunity and two distributed delays is proposed and analyzed. Two bifurcation parameters, the basic reproduction number, [Formula: see text] and the humoral immunity number, [Formula: see text] are derived. We established a set of conditions on the general functions which are sufficient to determine the global dynamics of the model. Utilizing Lyapunov functions and LaSalle’s invariance principle, the global asymptotic stability of all equilibria of the model is obtained. An example is presented and some numerical simulations are conducted in order to illustrate the dynamical behavior.

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.

Global dynamics of an age-structured viral infection model with general incidence function and absorption

2018 ◽  
Vol 11 (05) ◽  
pp. 1850065 ◽  
Author(s):  
Khalid Hattaf ◽  
Yu Yang
Keyword(s):  
Viral Infection ◽  
Infection Model ◽  
Uniform Persistence ◽  
Global Dynamics ◽  
Incidence Function ◽  
Proposed Model ◽  
Viral Particles ◽  
Age Structured ◽  
Well Posed ◽  
Viral Infection Model

In this paper, we propose an age-structured viral infection model with general incidence function that takes account of the loss of viral particles due to their absorption into susceptible cells. The proposed model is described by partial differential and ordinary differential equations. We first show that the model is mathematically and biologically well-posed. Furthermore, the uniform persistence and the global behavior of the model are investigated. Moreover, the age-structured models and results presented in many previous studies are improved and generalized.

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