scholarly journals Globale Stability in a Viral Infection Model with Beddington-DeAngelis Functional Response

2015 ◽  
Vol 9 (1) ◽  
pp. 27-29
Author(s):  
Wang Zhanwei ◽  
He Xia
Keyword(s):  
Lyapunov Function ◽  
Viral Infection ◽  
Functional Response ◽  
Reproduction Number ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
The Stability ◽  
Viral Infection Model ◽  
The Basic Reproduction Number

The stability of a mathematical model for viral infection with Beddington-DeAngelis functional response is considered in this paper. If the basic reproduction number R ≤1, by the Routh-Hurwitz criterion and Lyapunov function, the uninfected equilibrium E is globally asymptotically stable. Then, the global stability of the infected equilibrium E is obtained by the method of Lyapunov function

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.

scholarly journals Dynamics Analysis of a Viral Infection Model with a General Standard Incidence Rate

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yu Ji ◽  
Muxuan Zheng
Keyword(s):  
Viral Infection ◽  
Incidence Rate ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Reproduction Numbers ◽  
The Basic Reproduction Number ◽  
General Standard

The basic viral infection models, proposed by Nowak et al. and Perelson et al., respectively, have been widely used to describe viral infection such as HBV and HIV infection. However, the basic reproduction numbers of the two models are proportional to the number of total cells of the host's organ prior to the infection, which seems not to be reasonable. In this paper, we formulate an amended model with a general standard incidence rate. The basic reproduction number of the amended model is independent of total cells of the host’s organ. When the basic reproduction numberR0<1, the infection-free equilibrium is globally asymptotically stable and the virus is cleared. Moreover, ifR0>1, then the endemic equilibrium is globally asymptotically stable and the virus persists in the host.

scholarly journals Dynamics of a Viral Infection Model with General Contact Rate between Susceptible Cells and Virus Particles

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Chenxi Dai ◽  
Cui Ma ◽  
Lijuan Song ◽  
Kaifa Wang
Keyword(s):  
Viral Infection ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Host Cells ◽  
Infection Model ◽  
Contact Rate ◽  
Asymptotically Stable ◽  
Virus Particles ◽  
Viral Infection Model ◽  
The Basic Reproduction Number

This paper investigates the dynamic behavior of a viral infection model with general contact rate between susceptible host cells and free virus particles. If the basic reproduction number of the virus is less than unity, by LaSalle’s invariance principle, the disease-free equilibrium is globally asymptotically stable. If the basic reproduction number of the virus is greater than unity, then the virus persists in the host and the endemic equilibrium is locally asymptotically stable.

scholarly journals Stability Analysis for Viral Infection Model with Multitarget Cells, Beddington-DeAngelis Functional Response, and Humoral Immunity

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Xinxin Tian ◽  
Jinliang Wang
Keyword(s):  
Immune Response ◽  
Viral Infection ◽  
Incidence Rate ◽  
Functional Response ◽  
Humoral Immunity ◽  
Infection Model ◽  
Target Cells ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Viral Infection Model

We formulate a (2n+2)-dimensional viral infection model with humoral immunity,nclasses of uninfected target cells and  nclasses of infected cells. The incidence rate of infection is given by nonlinear incidence rate, Beddington-DeAngelis functional response. The model admits discrete time delays describing the time needed for infection of uninfected target cells and virus replication. By constructing suitable Lyapunov functionals, we establish that the global dynamics are determined by two sharp threshold parameters:R0andR1. Namely, a typical two-threshold scenario is shown. IfR0≤1, the infection-free equilibriumP0is globally asymptotically stable, and the viruses are cleared. IfR1≤1<R0, the immune-free equilibriumP1is globally asymptotically stable, and the infection becomes chronic but with no persistent antibody immune response. IfR1>1, the endemic equilibriumP2is globally asymptotically stable, and the infection is chronic with persistent antibody immune response.

scholarly journals Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 328 ◽  
Author(s):  
Yanli Ma ◽  
Jia-Bao Liu ◽  
Haixia Li
Keyword(s):  
Lyapunov Function ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, an SIQR (Susceptible, Infected, Quarantined, Recovered) epidemic model with vaccination, elimination, and quarantine hybrid strategies is proposed, and the dynamics of this model are analyzed by both theoretical and numerical means. Firstly, the basic reproduction number R 0 , which determines whether the disease is extinct or not, is derived. Secondly, by LaSalles invariance principle, it is proved that the disease-free equilibrium is globally asymptotically stable when R 0 < 1 , and the disease dies out. By Routh-Hurwitz criterion theory, we also prove that the disease-free equilibrium is unstable and the unique endemic equilibrium is locally asymptotically stable when R 0 > 1 . Thirdly, by constructing a suitable Lyapunov function, we obtain that the unique endemic equilibrium is globally asymptotically stable and the disease persists at this endemic equilibrium if it initially exists when R 0 > 1 . Finally, some numerical simulations are presented to illustrate the analysis results.

GLOBAL ANALYSIS OF A VIRAL INFECTION MODEL WITH APPLICATION TO HBV INFECTION

2010 ◽  
Vol 18 (02) ◽  
pp. 325-337 ◽  
Author(s):  
YU JI ◽  
LEQUAN MIN ◽  
YONGAN YE
Keyword(s):  
Viral Infection ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Global Analysis ◽  
Hiv Infections ◽  
Hbv Infection ◽  
Infection Model ◽  
Globally Asymptotically Stable ◽  
Reproduction Numbers ◽  
The Basic Reproduction Number

The basic models of within-host viral infection, proposed by Nowak and May2 and Perelson and Nelson,5 have been widely used in the studies of HBV and HIV infections. The basic reproduction numbers of the two models are proportional to the number of total cells of the host's organ prior to the infection. In this paper, we formulate an amended Perelson and Nelson's model with standard incidence. The basic reproduction number of the amended model is independent of total cells of the host's organ. If the basic reproduction number R0 < 1, then the infection-free equilibrium is globally asymptotically stable and the virus is cleared; if R0 > 1, then the virus persists in the host, and solutions approach either an endemic equilibrium or a periodic orbit. Numerical simulations of this model agree well with the clinical HBV infection data. This can provide a possible interpretation for the viral oscillation behaviors, which were observed in chronic HBV infection patients.

Global Dynamics of a HIV Infection Model with Delayed CTL Response and Cure Rate

2013 ◽  
Vol 791-793 ◽  
pp. 1322-1327
Author(s):  
Yan Yan Yang ◽  
Hui Wang ◽  
Zhi Xing Hu ◽  
Wan Biao Ma
Keyword(s):  
Infection Model ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Cure Rate ◽  
Globally Asymptotically Stable ◽  
Ctl Response ◽  
Stable Periodic ◽  
Hiv Infection Model ◽  
The Stability ◽  
Viral Infection Model

In this paper, we have considered a viral infection model with delayed CTL response and cure rate. For this model, we have researched the stability of these three equilibriums depend on two threshold parameters and , that is, if , the infected-free equilibrium is locally asymptotically stable; if , the infected equilibrium without CTL response is globally asymptotically stable; and if , the infected equilibrium exists, at he same time, we have found that the time delay can lead to Hopf bifurcations and stable periodic solutions when the is unstable.

scholarly journals On Oscillatory Pattern of Malaria Dynamics in a Population with Temporary Immunity

2007 ◽  
Vol 8 (3) ◽  
pp. 191-203 ◽  
Author(s):  
J. Tumwiine ◽  
J. Y. T. Mugisha ◽  
L. S. Luboobi
Keyword(s):  
Steady State ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Oscillatory Pattern ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number ◽  
Temporary Immunity

We use a model to study the dynamics of malaria in the human and mosquito population to explain the stability patterns of malaria. The model results show that the disease-free equilibrium is globally asymptotically stable and occurs whenever the basic reproduction number,R0is less than unity. We also note that whenR0>1, the disease-free equilibrium is unstable and the endemic equilibrium is stable. Numerical simulations show that recoveries and temporary immunity keep the populations at oscillation patterns and eventually converge to a steady state.

ANALYSIS OF AN AGE-STRUCTURED HIV-1 INFECTION MODEL WITH LOGISTIC TARGET CELL GROWTH

2020 ◽  
Vol 28 (04) ◽  
pp. 927-944
Author(s):  
HUIJUAN LIU ◽  
FEI XU ◽  
JIA-FANG ZHANG
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Logistic Growth ◽  
Infection Model ◽  
Target Cells ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Age Structured ◽  
Hiv 1 ◽  
The Basic Reproduction Number

In this work, we construct an age-structured HIV-1 infection model to investigate the interplay between [Formula: see text] cells and viruses. In our model, we assume that the variations in the death rate of productively infected [Formula: see text] cells and the production rate of virus in infected cells are all age-dependent, and the target cells follow logistic growth. We perform mathematical analysis and prove the persistence of the semi-flow of the system. We calculate the basic reproduction number and prove the local and global stability of the steady states. We show that if the basic reproduction number is less than one, the disease-free equilibrium is globally asymptotically stable, and if the basic reproduction number is greater than one, the infected steady state is locally asymptotically stable.

STABILITY OF AN AGE-STRUCTURED SEIS EPIDEMIC MODEL WITH INFECTIVITY IN INCUBATIVE PERIOD

2010 ◽  
Vol 03 (03) ◽  
pp. 299-312 ◽  
Author(s):  
SHU-MIN GUO ◽  
XUE-ZHI LI ◽  
XIN-YU SONG
Keyword(s):  
Epidemic Model ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Stability Conditions ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Age Structured ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, an age-structured SEIS epidemic model with infectivity in incubative period is formulated and studied. The explicit expression of the basic reproduction number R0 is obtained. It is shown that the disease-free equilibrium is globally asymptotically stable if R0 < 1, at least one endemic equilibrium exists if R0 > 1. The stability conditions of endemic equilibrium are also given.

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