Math 4600, Homework 6.2, due March 5
This part of the homework focuses on the HIV-model we last considered in
class: when the protease inhibitor completely blocks the production of infectious
virus particles. (As a side note: if you are wondering what happens when the
drug is assumed to be only patially effective, for a look at some rea data, and
much more information, see the review article posted under “Lecture material”
part of the class website.)
1. In an experiment the concentration of infectious viral particles VI (t) was
measured in one patient.
a) When plotted on a log-scale the graph was approximately linear with the
slope of -3.1 day−1 . Use these data to estimate value of c from the model
solution we obtained in class.
b) What is the half-life of virus particles with this parameter value? (half time
is the time in which he population reduces to half its initiial size)
2. Pre-treatment estimate of viral load in a patient was found to be 130×103
virus particles per ml of plasma.
a) What is the clearance rate of the virus per ml of plasma, using your estimate
of c from above?
b) At steady state, the production rate of the virus must equal its clearance
rate. What is the total viral production per day pre-treatment if the person’s
fluid volume is estimated to be 15 liters? This is a very high number of viruses
produced daily. When it was first estimated, it was a surprise.
3. It has been estimated from data that δ = 0.5 day−1 . Plot total number of
viruses V (t) as functions of time in regular and log-scale (assume same values for
c and V0 as above. Notice that there is a “shoulder” in the beginning, indicative
of a slower initial decay rate of V . Suggest a possible reason for this observation.
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