Subject: Closed Loop Problems

Posted by John F. Heinbokel on 11/12/2009
In Reply To:Closed Loop Problems Posted by Karl North on 11/10/2009

Message:

Hi Karl,

Sounds like things are going well for you on the college teaching front. I liked some of the points and examples you develop in your course and will track a couple of them down; I always love to steal good ideas!

You inquired about a human antibiotic resistance model. Couple things came to mind:

1. Jack Homer and colleagues published a paper on that topic in 2000 in the System Dynamics Review.

2. Long ago when we (Jeff Potash and I) were still at Trinity College, we put together a very simple population genetics model that was, on its surface, supposed to reflect the point mutation dynamics of Sickle Cell Anemia. In fact it works for any simple natural selection process, although there's not a lot of feedback in it. Basically, imagine a 2-allele gene.
In each generation we produce a fixed number of individuals with randomly distributed alleles in the proportion that survived the last generation.
Then we apply natural selective mortality fractions to the three possible genomes, get a new gene frequency, and produce a new generation with that new frequency. If you call one of the alleles 'antibiotic resistance' and apply the mortality fractions reasonably, you can see the growth (or
decline) of that resistance gene. I'll track down your e-mail address and take the liberty of sending you that. If it doesn't meet your needs, you can dump it.

3. More ambitiously once upon a time Jeff and I put together a set of 10 case-studies that looked at the Biology and History of Smallpox (History and Biology ..., if Jeff's describing it!). One of the five biologically focused case studies used smallpox as a template to look at three population genetics questions: host (human) resistance evolution; virulence evolution in the virus; and development of antibiotic resistance (yeah, I know - a virus like Variola doesn't respond to antibiotics). That's a much bigger and more elaborate package. I'll be happy to send it to you, but will wait to be asked, rather than just inflict it on you.

Thanks for your contribution to this List.

john