438 research outputs found
Transition between immune and disease states in a cellular automaton model of clonal immune response
In this paper we extend the Celada-Seiden (CS) model of the humoral immune
response to include infectious virus and cytotoxic T lymphocytes (cellular
response). The response of the system to virus involves a competition between
the ability of the virus to kill the host cells and the host's ability to
eliminate the virus. We find two basins of attraction in the dynamics of this
system, one is identified with disease and the other with the immune state.
There is also an oscillating state that exists on the border of these two
stable states. Fluctuations in the population of virus or antibody can end the
oscillation and drive the system into one of the stable states. The
introduction of mechanisms of cross-regulation between the two responses can
bias the system towards one of them. We also study a mean field model, based on
coupled maps, to investigate virus-like infections. This simple model
reproduces the attractors for average populations observed in the cellular
automaton. All the dynamical behavior connected to spatial extension is lost,
as is the oscillating feature. Thus the mean field approximation introduced
with coupled maps destroys oscillations.Comment: 27 pages LaTeX + 7 Figures Postscrip
Modeling the dynamics of viralāhost interaction during treatment of productively infected cells and free virus involving total immune response
Virus dynamics models are useful in interpreting and predicting the change in viral load over the time and the effect of treatment in emerging viral infections like HIV/AIDS, hepatitis B virus (HBV).We propose a mathematical model involving the role of total immune response (innate, CTL, and humoral) and treatment for productively infected cells and free virus to understand the dynamics of virusāhost interactions. A threshold condition for the extinction or persistence of infection, i.e. basic reproductive number, in the presence of immune response (RI ) is established. We study the global stability of virus-free equilibrium and interior equilibrium using LaSalleās principle and Lyapunovās direct method. The global stability of virus-free equilibrium ensures the clearance of virus from the body, which is independent of initial status of subpopulations. Central manifold theory is used to study the behavior of equilibrium points at RI = 1, i.e. when the basic reproductive number in the presence of immune response is one. A special case, when the immune response (IR) is not present, has also been discussed. Analysis of special case suggests that the basic reproductive number in the absence of immune response R0 is greater than that of in the presence of immune response RI , i.e. R0> RI . It indicates that infection may be eradicated if RI < 1. Numerical simulations are performed to illustrate the analytical results using MatLab and Mathematica
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