From slawomir@math.utk.edu Thu Mar 16 17:28:57 1995
From: Slawomir Kolodynski <slawomir@math.utk.edu>
Date: Thu, 16 Mar 1995 17:29:06 -0500


Slawek Kolodynski - Modeling Note

In her note on cross-strain immunity Brenda wrote:

" On friday we discussed a model with
a susceptible population (S) and two types of infected populations,
I1 and I2, where I2 was infected with an ABx resistant strain.  Although
we didn't draw them in, I think there may need to be an arrow from
bot I1 to box I2, representing mutation of the strain to the ABx
resistant form."

I couldn't agree more. I think the arrow between I1 and I2 is the main
concept in the model. Otherwise if we start from the initial conditions
I1>0, I2=0 we would never get any people infected with the resistant strain,
which we know is not the case: resistant strains do exist.

By the way, I think it is better to call these groups I0 and I1 (0 for zero
resistance, 1 for full resistance). May be one day we will consider a model
with partial resistance, say I(0.5), or even with a continuous spectrum of
resistance, then we would have a consistent notation.

" We may also need an arrow from box I2 to I1,
representing the competitive advantage of the I1 strain (because of the
cost associated with the resistant strain).  This would be a
function of the pop. size I2 and antibiotic ise (as Abx use increases,
transfer from box I2 to Box I1 decreases)."

My opinion is different. This arrow from I2 to I1 would represent the people,
who were infected with the resistant strain and suddenly became infected with
a non resistant strain. I don't think it is possible, even with the level
of use of Abx equal to zero. Once you get the resistant strain, you cannot 
make it not resistant. 
I think the competitive advantage of I1 strain may be build in
 the model in a different way. Namely, we can set the number of people who move
from S to I1 as geater than from S to I2 (relative to the values of S*I1 and
S*I2). It would mean that I2 spreads more slowly in the population, for example
smaller fraction of interactions between I2 and S ends with infection, than
between S and I1.
This way has one more advantage: even if it is not true that I1 has the
competitive advantage, we can say that we isolate better the patients with
the resistant strain MAKING this assumption true.


Slawek Kolodynski