2 Sep 2011 nutella   » (Master)

Cruising the library's "New" shelf yielded Jennifer Ouellette's The Calculus Diaries. I grabbed that because I am very much an amateur mathematician and so always hope for that "Aha!" moment from a new teacher, and I also like reading about the history of mathematics. The book is heavy on Diary (is she sponsored by Toyota?) and light on Calculus but some of the anecdotes were fun. For example, even though my job involves mathematical modeling of populations (people or cells or molecules) I had missed the 2009 paper by Munz and colleagues in Infectious Disease Modelling Progress called When Zombies Attack!.

Ms. Ouellette's coverage doesn't leap straight into Kermack & McKendrick's 1927 paper on the SIR model, but instead steps back to simple population modeling with Thomas Malthus (1798, unrestricted exponential growth) and Pierre-Fran├žois Verhulst (1838, logistic model). However, history is more rich than the space in the book will support, so it isn't pointed out that it took until 1920 before Pearl & Reed rediscovered the logistic equation and used it to model US population growth. The material that is really missing is when cool things start to happen, both mathematically and historically, when we moved away from linear algebraic models and over to multi-equation (compartmental) interacting nonlinear systems. Alfred Lotka buried that approach in his 1925 textbook (mainly applying it to chemical reactions) but it came more to the fore when Vito Volterra discovered it (apparently) independently and published it in 1926 when describing fish population dynamics (Dr. Lotka's letter to the journal, pointing out Prof. Volterra's oversight, is politely understated). While Kermack & McKendrick were applying Lotka-Volterra, it was made more rigorous by the work of Georgii Gause (1932) and Andrey Kolmogorov (1936). Then Kermack/McKendrick seems to be forgotten for a while, until it was popularized more recently by e.g. Prof. Roy Anderson. These days, in the medical world, this kind of model is not just limited to epidemiological disease modeling (and prevention strategies) but can also be used to model interactions between pathogens and cells within the body (e.g. the groups of Prof. Alan Perelson at Los Alamos and Prof. Martin Nowak at Harvard).

Also, thanks to Ms. Ouellette, having finished her book I am now reading Seth Grahame-Smith's Pride and Prejudice and Zombies (but not a Choc-ice to be found...)

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