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.

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.

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.

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 Global Dynamics of a Stochastic Viral Infection Model with Latently Infected Cells

2021 ◽  
Vol 11 (21) ◽  
pp. 10484
Author(s):  
Chinnathambi Rajivganthi ◽  
Fathalla A. Rihan
Keyword(s):  
Viral Infection ◽  
Global Solutions ◽  
Infection Model ◽  
Global Dynamics ◽  
Large Intensity ◽  
Ergodic Distribution ◽  
Latently Infected ◽  
Infected Cells ◽  
White Noises ◽  
Viral Infection Model

In this paper, we study the global dynamics of a stochastic viral infection model with humoral immunity and Holling type II response functions. The existence and uniqueness of non-negative global solutions are derived. Stationary ergodic distribution of positive solutions is investigated. The solution fluctuates around the equilibrium of the deterministic case, resulting in the disease persisting stochastically. The extinction conditions are also determined. To verify the accuracy of the results, numerical simulations were carried out using the Euler–Maruyama scheme. White noise’s intensity plays a key role in treating viral infectious diseases. The small intensity of white noises can maintain the existence of a stationary distribution, while the large intensity of white noises is beneficial to the extinction of the virus.

Sign in / Sign up

Export Citation Format

Share Document