scholarly journals Global dynamics of an age-structured in-host viral infection model with humoral immunity

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Liangchen Li ◽  
Rui Xu
Keyword(s):  
Viral Infection ◽  
Humoral Immunity ◽  
Infection Model ◽  
Global Dynamics ◽  
Age Structured ◽  
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.

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.

scholarly journals A Fractional Order Model for Viral Infection with Cure of Infected Cells and Humoral Immunity

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Adnane Boukhouima ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Viral Infection ◽  
Humoral Immunity ◽  
Host Cells ◽  
Infection Model ◽  
Order Model ◽  
Fractional Order Model ◽  
Infected Cells ◽  
Fractional Differential ◽  
Well Posed ◽  
Viral Infection Model

In this paper, we study the dynamics of a viral infection model formulated by five fractional differential equations (FDEs) to describe the interactions between host cells, virus, and humoral immunity presented by antibodies. The infection transmission process is modeled by Hattaf-Yousfi functional response which covers several forms of incidence rate existing in the literature. We first show that the model is mathematically and biologically well-posed. By constructing suitable Lyapunov functionals, the global stability of equilibria is established and characterized by two threshold parameters. Finally, some numerical simulations are presented to illustrate our theoretical analysis.

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.

Sign in / Sign up

Export Citation Format

Share Document