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Description:
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Stochastic models are formulated and applied to intra -host viral and cellular dynamics .
Specifically , two Itˆo stochastic differential equation models for early viral
infection of host cells are formulated . The stochastic models are based on an underlying
deterministic model that was originally formulated for Human Immunodeficiency
Virus , type 1 (HIV -1 ) , the most common strain of the virus . However , the deterministic
and stochastic models apply to more general viral infections , during the early
stages of infection , prior to activation of the immune response . The underlying deterministic
model is a system of ordinary differential equations (ODEs ) that includes
variables for the healthy CD4+ T cells , the target cells of HIV -1 , latently infected T
cells , actively infected T cells and free virions . The first stochastic model assumes
that after viral entry into the host cell and subsequent reproduction , the virus bursts
from the cell , killing the host cell (burst model ) . The second model assumes the virus
continually buds off from the host cell until the infected cell dies (budding model ) .
The basic reproduction number R0 is calculated for the underlying deterministic
model and it is shown that if R0 < 1 , then the disease -free equilibrium (DFE ) is both
locally and globally asymptotically stable . For the stochastic models , application of
Itˆo’s formula allows calculation of the moments corresponding to the distributions in
the stochastic models . Because the moment differential equations form an infinite
system of differential equations , each moment depending on higher -order moments ,
they cannot be solved unless some distributional assumption is made . Under the
assumption of normality , the mean and variance for the target cell population are
calculated . Numerical examples compare the dynamics of the deterministic model
to the mean of the two stochastic models when R0 > 1 . In addition , the standard
deviation is computed and compared in the stochastic models |