I have been looking at an interesting book "Pharmacokinetic-Pharmacodynamic Modeling and Simulation" by Peter Bonate on pharmacokinetic models: the models of how medical drugs work their way through the tissues and organs of a human body, etc.

The book discusses "mechanistic" models where systems of differential equations model individual process in the body such as cellular metabolism or the drug, the operation of enzymes, etc. But these types of mechanistic models are used in many fields, such as hydrology to model flooding processes, weather forecasting, earthquake models, models for structural engineering to see how buildings will respond to different physical forces, etc.

While I have found some subject specific books on this topic, I was wondering if anyone knew of a good book or two on designing these types of mechanistic models? Given that these models have a relatively general form--such as large systems of equations--these models must face similar issues when it comes to calibrating against data, numerical methods, goodness of fit analysis, etc. dealing with multiple time-scales, etc.

Can anyone suggest a book that covers these topics across mechanistic models. Or even if someone know of good books within a particular subject area, that would be helpful. I was just hoping to standardize my own approaches to a problem I am working on.

  • $\begingroup$ I'm not sure there's a great book on the topic. The full story is spread around in a ton of primary sources. $\endgroup$ Sep 28 '19 at 18:53
  • $\begingroup$ Haha, hey @ChrisRackauckas I end up talking to you everywhere. Yeah, the Bonate book is pretty good, and I think there are a few more decent ones. Perhaps it is a good idea to create a community wiki for this topic, since there is no clear baseline texts, etc. If you know of any good books from your areas of work, please include them. I can look into the community wiki thing. $\endgroup$
    – krishnab
    Sep 28 '19 at 18:59
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    $\begingroup$ Uri Alon's Systems Biology book is also pretty good. Murray's Mathematical Biology I and II are pretty good. Leah Edelstein-Keshet's is another one I'd grab.That's just a bunch of biology. I don't know of a good resource on model fitting issues, but then again, I don't know of great primary literature on it either. There's a lot of details that seem to go unmentioned. $\endgroup$ Sep 28 '19 at 19:40
  • $\begingroup$ @ChrisRackauckas these are all good book. I have not read Leah Edelstein-Keshet's book though, so I will check that one out. I also liked Wilkinson's book "Stochastic Modelling for Systems Biology" which has a lot of good discussion. There are probably a few more that I need to look up the citations for. $\endgroup$
    – krishnab
    Sep 28 '19 at 20:57

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