Global dynamics of cell mediated immunity in viral infection models with distributed delays

  title={Global dynamics of cell mediated immunity in viral infection models with distributed delays},
  author={Yukihiko Nakata},
  journal={arXiv: Dynamical Systems},
  • Y. Nakata
  • Published 15 August 2010
  • Mathematics, Biology
  • arXiv: Dynamical Systems
In this paper, we investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in \textit{vivo}. The model has two distributed time delays describing time needed for infection of cell and virus replication. Our model admits three possible equilibria, an uninfected equilibrium and infected equilibrium with or without immune response depending on the basic reproduction number for viral infection $R_{0}$ and for CTL response $R_{1}$ such that… Expand
Global stability of in-host viral models with humoral immunity and intracellular delays
Investigating the dynamical behavior of in-host viral models with humoral immunity and intracellular delays finds that the global dynamics are determined by two threshold parameters R0 and R1, which indicate that the infection becomes chronic but with no persistent B cells response. Expand
Global threshold dynamics in a five-dimensional virus model with cell-mediated, humoral immune responses and distributed delays
The dynamics of a five-dimensional virus model with immune responses and an intracellular delay which describes the interactions of the HIV virus, CD4 cells and CTLs within host is investigated. Expand
Effect of cell-mediated , humoral immune responses on global dynamics of a delayed virus infection model
For modeling disease progression scenarios, dividing population into compartments has been recognized as a common approach due to attempts to predict final size of epidemics [10]. With compartmentsExpand
Global properties of a cell mediated immunity in HIV infection model with two classes of target cells and distributed delays
The method of Lyapunov functional is used and it is proven that if R0 ≤ 1, then the uninfected steady state is globally asymptotically stable (GAS), if , then the infected steady state without CTL immune response is GAS, and if . Expand
A class of delayed viral infection models with general incidence rate and adaptive immune response
Three generalized models that describe the interactions between virus, host cells, antibodies and cytotoxic T lymphocytes (CTL) cells and several viral infection models with discrete, finite and infinite distributed delays existing in other previous studies are extended and generalized. Expand
It is proven that if the basic reproduction number R0 is less than R0, the global asymptotic stability of the uninfected and infected steady states of the HIV infection models can be established. Expand
Stability analysis in delayed within-host viral dynamics with both viral and cellular infections
Abstract We consider a within-host viral model by incorporating (i) mitosis of the healthy target cells which is described by the logistic term; (ii) two routes of infection via, respectively,Expand
Global threshold dynamics in an HIV virus model with nonlinear infection rate and distributed invasion and production delays.
  • Zhaohui Yuan, X. Zou
  • Mathematics, Medicine
  • Mathematical biosciences and engineering : MBE
  • 2013
The model has the threshold dynamics: if the basic reproduction number (BRN) is less than or equal to one, then the infection free equilibrium is globally asymptotically stable, meaning that HIV virus will be cleared and the viral concentration will approach a positive constant level. Expand
Global analysis of a virus infection model with multitarget cells and distributed intracellular delays
It is proven that if the basic reproduction number is less than unity then the uninfected steady state is global asymptotically stable, and if the infected steady state exists then it is globally asymptonically stable. Expand
Global properties for virus dynamics model with mitotic transmission and intracellular delay
Abstract In this paper we study the basic model of viral infections with mitotic transmission and intracellular delay discrete. The delay corresponds to the time between infection of uninfected cellsExpand


Impact of Intracellular Delays and Target-Cell Dynamics on In Vivo Viral Infections
The dynamics of an in-host model with general form of target-cell dynamics, nonlinear incidence, and distributed delay, which can describe the in vivo infection dynamics of many viruses such as HIV-I, HCV, and HBV, are investigated. Expand
In this paper, we consider a mathematical model for HIV-1 infection with intracellular delay and cell-mediated immune response. A novel feature is that both cytotoxic T lymphocytes (CTLs) and theExpand
Global Dynamics of an In-host Viral Model with Intracellular Delay
It is proved that the chronic-infection equilibrium is globally asymptotically stable when R0>1, and it is shown that for intercellular delays to generate sustained oscillations in in-host models it is necessary have a logistic mitosis term in target-cell compartments. Expand
Impact of delays in cell infection and virus production on HIV-1 dynamics.
  • Huiyan Zhu, X. Zou
  • Biology, Medicine
  • Mathematical medicine and biology : a journal of the IMA
  • 2008
The formula foralysed is a mathematical model for HIV-1 infection with two delays accounting for a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and shows that increasing either of the two delays will decrease. Expand
A chronic viral infection model with immune impairment.
Therapy could shift the patient from a disease progression to an immune control outcome, despite that the therapy is not necessarily lifelong, and this would allow the immune response to control the virus in the long term even in the absence of continued therapy. Expand
Asymptotic properties of a HIV-1 infection model with time delay
Based on some important biological meanings, a class of more general HIV-1 infection models with time delay is proposed in the paper. In the HIV-1 infection model, time delay is used to describe theExpand
Population Dynamics of Immune Responses to Persistent Viruses
A simple mathematical approach is developed to explore the relation between antiviral immune responses, virus load, and virus diversity in infections with the human T cell leukemia virus and the human immunodeficiency virus. Expand
Stability analysis of delay differential equation models of HIV-1 therapy for fighting a virus with another virus
Considering two kinds of delays accounting, respectively, for (i) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and (ii)Expand
Influence of delayed viral production on viral dynamics in HIV-1 infected patients.
It is demonstrated that it is possible to incorporate distributed intracellular delays into existing models for HIV dynamics and to use these refined models to estimate the half-life of free virus from data on the decline in HIV-1 RNA following treatment. Expand
Complex dynamic behavior in a viral model with delayed immune response
The rich dynamics of a viral infection model is studied under the assumption that the immune response is retarded. It is shown that if the basic reproductive ratio of the virus is less than one, theExpand