       Problem with a system of equations describing an exposure to lead...

• To: mathgroup at smc.vnet.net
• Subject: [mg50375] Problem with a system of equations describing an exposure to lead...
• From: Richard Palmer <dickp at bellatlantic.net>
• Date: Tue, 31 Aug 2004 06:28:57 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```I have a system of equations

Eqns={u[t]==a bl[t-1],
bo[t]==b bl[t-1]-c bo[t-1],
bl[t]==(1-a-b) bl[t-1]-c bo[t-1],
u==0,
bo==0,
bl==pb}

They are supposed to represent a system of what happens when a person
suffers a one-time exposure to lead (pb).  At any given time, the person
will pass some portion of the lead that is in the blood and soft tissue
(bl[t]) through the urine (u[t]) while some portion moves to the bone
(bo[t]) and a small portion moves from the bone back into the blood.  This
is easily solved with RSolve.  However,  I am concerned the solution may not
be correct:  I believe that for any time t, the amount of lead in the bone
and blood less all lead passed to date through the urine should equal the
level of exposure (pb).  Taking the Rsolve solutions and making a table of
u[t], bl[t], and bo[t] for times 0-5 will show the problem (substitute
random fractions for a,b, and c and take pb to be 1).  Is the mistake in the
solution or in my formulation of the model?  I am using Mathematica 5.