Dynamics of virus infection models with density-dependent diffusion and Beddington-DeAngelis functional response

2017 ◽  
Vol 40 (15) ◽  
pp. 5593-5612 ◽  
Author(s):  
Shaoli Wang ◽  
Jiafang Zhang ◽  
Fei Xu ◽  
Xinyu Song
Keyword(s):  
Virus Infection ◽  
Functional Response ◽  
Density Dependent ◽  
Infection Models

scholarly journals Dynamics of virus infection models with density-dependent diffusion

2017 ◽  
Vol 74 (10) ◽  
pp. 2403-2422 ◽  
Author(s):  
Shaoli Wang ◽  
Jiafang Zhang ◽  
Fei Xu ◽  
Xinyu Song
Keyword(s):  
Virus Infection ◽  
Density Dependent ◽  
Infection Models

scholarly journals Caenorhabditis elegans as an Emerging Model for Virus-Host Interactions

2017 ◽  
Vol 91 (23) ◽  
Author(s):  
Don B. Gammon
Keyword(s):  
Caenorhabditis Elegans ◽  
Virus Infection ◽  
Fungal Pathogens ◽  
Model Organism ◽  
Artificial Infection ◽  
Viral Pathogen ◽  
Content Type ◽  
Host Interactions ◽  
C Elegans ◽  
Infection Models

ABSTRACT Since 1999, Caenorhabditis elegans has been extensively used to study microbe-host interactions due to its simple culture, genetic tractability, and susceptibility to numerous bacterial and fungal pathogens. In contrast, virus studies have been hampered by a lack of convenient virus infection models in nematodes. The recent discovery of a natural viral pathogen of C. elegans and development of diverse artificial infection models are providing new opportunities to explore virus-host interplay in this powerful model organism.

Stability and Hopf Bifurcation of a Delayed Density-Dependent Predator–Prey System with Beddington–DeAngelis Functional Response

2016 ◽  
Vol 26 (10) ◽  
pp. 1650165 ◽  
Author(s):  
Haiyin Li ◽  
Gang Meng ◽  
Zhikun She
Keyword(s):  
Hopf Bifurcation ◽  
Density Dependence ◽  
Functional Response ◽  
Positive Equilibrium ◽  
Stability Switches ◽  
Predator Prey ◽  
Geometric Criterion ◽  
Density Dependent ◽  
Prey System ◽  
The Stability

In this paper, we investigate the stability and Hopf bifurcation of a delayed density-dependent predator–prey system with Beddington–DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered such that the studied predator–prey system conforms to the realistically biological environment. We start with the geometric criterion introduced by Beretta and Kuang [2002] and then investigate the stability of the positive equilibrium and the stability switches of the system with respect to the delay parameter [Formula: see text]. Especially, we generalize the geometric criterion in [Beretta & Kuang, 2002] by introducing the condition [Formula: see text] which can be assured by the condition [Formula: see text], and adopting the technique of lifting to define the function [Formula: see text] for alternatively determining stability switches at the zeroes of [Formula: see text]s. Afterwards, by the Poincaré normal form for Hopf bifurcation in [Kuznetsov, 1998] and the bifurcation formulae in [Hassard et al., 1981], we qualitatively analyze the properties for the occurring Hopf bifurcations of the system (3). Finally, an example with numerical simulations is given to illustrate the obtained results.

scholarly journals Stability of Virus Infection Models with Antibodies and Chronically Infected Cells

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Mustafa A. Obaid ◽  
A. M. Elaiw
Keyword(s):  
Immune Response ◽  
Steady State ◽  
Virus Infection ◽  
Incidence Rate ◽  
Lyapunov Functions ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Infection Models ◽  
Infected Cells

Two virus infection models with antibody immune response and chronically infected cells are proposed and analyzed. Bilinear incidence rate is considered in the first model, while the incidence rate is given by a saturated functional response in the second one. One main feature of these models is that it includes both short-lived infected cells and chronically infected cells. The chronically infected cells produce much smaller amounts of virus than the short-lived infected cells and die at a much slower rate. Our mathematical analysis establishes that the global dynamics of the two models are determined by two threshold parametersR0andR1. By constructing Lyapunov functions and using LaSalle's invariance principle, we have established the global asymptotic stability of all steady states of the models. We have proven that, the uninfected steady state is globally asymptotically stable (GAS) ifR0<1, the infected steady state without antibody immune response exists and it is GAS ifR1<1<R0, and the infected steady state with antibody immune response exists and it is GAS ifR1>1. We check our theorems with numerical simulation in the end.

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