Deterministic and Stochastic models for early viral infection within a host

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Title: Deterministic and Stochastic models for early viral infection within a host
Author: Vidurupola, Sukhitha W.
Abstract: 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
URI: http : / /hdl .handle .net /2346 /ETD -TTU -2010 -12 -1094
Date: 2010-12

Citation

Deterministic and Stochastic models for early viral infection within a host. Master's thesis, Texas Tech University. Available electronically from http : / /hdl .handle .net /2346 /ETD -TTU -2010 -12 -1094 .

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