106 research outputs found
Global dynamics of cell mediated immunity in viral infection models with distributed delays
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
and for CTL response such that . It is shown that
there always exists one equilibrium which is globally asymptotically stable by
employing the method of Lyapunov functional. More specifically, the uninfected
equilibrium is globally asymptotically stable if , an infected
equilibrium without immune response is globally asymptotically stable if
and an infected equilibrium with immune response is globally
asymptotically stable if . The immune activation has a positive role
in the reduction of the infection cells and the increasing of the uninfected
cells if .Comment: 16 pages, accepted by Journal of Mathematical Analysis and
Application
Global properties of an age-structured virus model with saturated antibody immune response, multi-target cells and general incidence rate
Some viruses, such as human immunodeficiency virus, can infect several types
of cell populations. The age of infection can also affect the dynamics of
infected cells and production of viral particles. In this work, we study a
virus model with infection-age and different types of target cells which takes
into account the saturation effect in antibody immune response and a general
non-linear infection rate. We construct suitable Lyapunov functionals to show
that the global dynamics of the model is completely determined by two critical
values: the basic reproduction number of virus and the reproductive number of
antibody response
GLOBAL ANALYSIS OF CELL INFECTION AND VIRUS PRODUCTION ON HIV-1 DYNAMICS
More than one sub-type of HIVs have been identified. This raises an issue of co-infections by multiple strains of HIVs. In this thesis, we propose two mathematical models, one ignoring intracellular delay and the other incorporating the delay, to describe the interactions of the populations of CD4+cells and two HIV stains. By nature, the two strains compete for CD4+ cells to invade for their own replications. By analyzing the two models, we find that the models demonstrate threshold dynamics: if the overall basic reproduction number Ro \u3c 1, then the infection free equilibrium is globally asymptotically stable; when R0 \u3e 1, then the competition exclusion principle generically holds in the sense that, except for the critical case R\ = R2 \u3e 1 where /?, is the individual basic reproduction number for strain i, all biologically meaningful solutions will converge to the single infection equilibrium representing the winning of the strain that has greater individual basic reproduction number. Numerical simulations are also performed to illustrate the theoretical results. The results on the model with delay also show that the basic reproduction number will be over calculated if the cellular delay is ignored
Viral in-host infection model with two state-dependent delays: stability of continuous solutions
summary:A virus dynamics model with two state-dependent delays and logistic growth term is investigated. A general class of nonlinear incidence rates is considered. The model describes the in-host interplay between viral infection and CTL (cytotoxic T lymphocytes) and antibody immune responses. The wellposedness of the model proposed and Lyapunov stability properties of interior infection equilibria which describe the cases of a chronic disease are studied. We choose a space of merely continuous initial functions which is appropriate for therapy, including drug administration
Impact of delay on HIV-1 dynamics of fighting a virus with another virus
In this paper, we propose a mathematical model for HIV-1 infection with
intracellular delay. The model examines a viral-therapy for controlling
infections through recombining HIV-1 virus with a genetically modified virus.
For this model, the basic reproduction number are identified
and its threshold properties are discussed. When , the
infection-free equilibrium is globally asymptotically stable. When
, becomes unstable and there occurs the
single-infection equilibrium , and and exchange their
stability at the transcritical point . If , where is a positive constant explicitly depending on the model
parameters, is globally asymptotically stable, while when , loses its stability to the double-infection equilibrium .
There exist a constant such that is asymptotically stable if
, and and exchange their stability at the
transcritical point . We use one numerical example to
determine the largest range of for the local stability of
and existence of Hopf bifurcation. Some simulations are performed to support
the theoretical results. These results show that the delay plays an important
role in determining the dynamic behaviour of the system. In the normal range of
values, the delay may change the dynamic behaviour quantitatively, such as
greatly reducing the amplitudes of oscillations, or even qualitatively changes
the dynamical behaviour such as revoking oscillating solutions to equilibrium
solutions. This suggests that the delay is a very important fact which should
not be missed in HIV-1 modelling
Global stability of vaccine-age/staged-structured epidemic models with nonlinear incidence
We consider two classes of infinitely dimensional epidemic models with nonlinear incidence, where one assumes that the rate of a vaccinated individual losing immunity depends on the vaccine-age and another assumes that, before the vaccine begins to wane, there is a period during which the vaccinated individuals have complete immunity against the infection. The first model is given by a coupled ordinary-hyperbolic differential system and the second class is described by a delay differential system. We calculate their respective basic reproduction numbers, and show they characterize the global dynamics by constructing the appropriate Lyapunov functionals
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