Global attractivity of a nonlocal reaction-diffusion viral infection model

2021 ◽  
pp. 1
Author(s):  
Yu Yang ◽  
Lan Zou ◽  
Cheng-Hsiung Hsu
Keyword(s):  
Viral Infection ◽  
Global Attractivity ◽  
Reaction Diffusion ◽  
Infection Model ◽  
Nonlocal Reaction ◽  
Viral Infection Model

A delayed reaction–diffusion viral infection model with nonlinear incidences and cell-to-cell transmission

2021 ◽  
Author(s):  
Qing Ge ◽  
Xia Wang ◽  
Libin Rong
Keyword(s):  
Viral Infection ◽  
Traveling Wave Solutions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Infection Model ◽  
Threshold Dynamics ◽  
Delayed Reaction ◽  
Homogeneous Neumann Boundary Condition ◽  
Cell Transmission ◽  
Viral Infection Model

In this paper, we propose a reaction–diffusion viral infection model with nonlinear incidences, cell-to-cell transmission, and a time delay. We impose the homogeneous Neumann boundary condition. For the case where the domain is bounded, we first study the well-posedness. Then we analyze the local stability of homogeneous steady states. We establish a threshold dynamics which is completely characterized by the basic reproduction number. For the case where the domain is the whole Euclidean space, we consider the existence of traveling wave solutions by using the cross-iteration method and Schauder’s fixed point theorem. Finally, we study how the speed of spread in space affects the spread of cells and viruses. We obtain the existence of the wave speed, which is dependent on the diffusion coefficient.

A stochastic viral infection model with general functional response

2016 ◽  
Vol 4 ◽  
pp. 435-445 ◽  
Author(s):  
Marouane Mahrouf ◽  
El Mehdi Lotfi ◽  
Mehdi Maziane ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Viral Infection ◽  
Functional Response ◽  
Infection Model ◽  
Viral Infection Model

scholarly journals Analysis of a diffusive cholera model incorporating latency and bacterial hyperinfectivity

2021 ◽  
Vol 20 (11) ◽  
pp. 3921
Author(s):  
Wei Yang ◽  
Jinliang Wang
Keyword(s):  
Lyapunov Functional ◽  
Global Attractivity ◽  
Reproduction Number ◽  
Reaction Diffusion ◽  
Threshold Dynamics ◽  
Positive Equilibrium ◽  
Flux Boundary Condition ◽  
Nonlocal Reaction ◽  
Theoretical Results ◽  
The Basic Reproduction Number

<p style='text-indent:20px;'>In this paper, we are concerned with the threshold dynamics of a diffusive cholera model incorporating latency and bacterial hyperinfectivity. Our model takes the form of spatially nonlocal reaction-diffusion system associated with zero-flux boundary condition and time delay. By studying the associated eigenvalue problem, we establish the threshold dynamics that determines whether or not cholera will spread. We also confirm that the threshold dynamics can be determined by the basic reproduction number. By constructing Lyapunov functional, we address the global attractivity of the unique positive equilibrium whenever it exists. The theoretical results are still hold for the case when the constant parameters are replaced by strictly positive and spatial dependent functions.</p>

Stability of a CD4+ T cell viral infection model with diffusion

2018 ◽  
Vol 11 (05) ◽  
pp. 1850071 ◽  
Author(s):  
Zhiting Xu ◽  
Youqing Xu
Keyword(s):  
T Cell ◽  
Viral Infection ◽  
Lyapunov Functions ◽  
Threshold Value ◽  
Endemic Equilibrium ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
The Stability ◽  
Viral Infection Model

This paper is devoted to the study of the stability of a CD[Formula: see text] T cell viral infection model with diffusion. First, we discuss the well-posedness of the model and the existence of endemic equilibrium. Second, by analyzing the roots of the characteristic equation, we establish the local stability of the virus-free equilibrium. Furthermore, by constructing suitable Lyapunov functions, we show that the virus-free equilibrium is globally asymptotically stable if the threshold value [Formula: see text]; the endemic equilibrium is globally asymptotically stable if [Formula: see text] and [Formula: see text]. Finally, we give an application and numerical simulations to illustrate the main results.

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