LabKitty Recommends: Mathematics of Epidemics on Networks -- Kiss et al.

All cultures need a foundational document. A kind of explanation of the world cum moral compass. Comfort for when the night is dark and full of terrors but the cable is out so HBO can't distract you with Carice van Houten's magnificent boobies. Something to shelter inside while you are sheltering inside.

But what? we reasonably ask. Christians have the Bible, Republicans have Machiavelli's Prince, barnyard animals have The Art of the Deal. What selection is available for the average punter trying to make sense of current events?

LabKitty recommends Mathematics of Epidemics on Networks. Not a phrase I ever expected to write, what with having experienced an actual epidemic on a network, but I think you browlf the context.

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The topic is an amalgam of two topics, those topics being epidemiology and graph theory. I once took a course on graph theory and had the temerity to ask the prof what it was good for (after grades were posted, natch). The question left him flummoxed (and rather cross).

Welp, I now have my answer. Graph theory isn't just for traveling salesmen and minimizing bridge crossings into Marburg (home of Marburg virus, and be thankful COVID isn't that). It also predicts the end of the world. You know those oh-so-clever nerd shirts with God said [Maxwell's equations] and there was light? To that we can add God said ∂_tu(t,z) = ½ ∂_zz(g(z)u(t,z))−∂_z(h(z)u(t,z)) and all returned to darkness. Or at least sat home and spendeth His 401K after His benes runneth out.

That equation describes the dynamics of an epidemic on a (large) network. But if you have no interest in epidemiology, know that Kiss et al. have produced a surprisingly accessible introduction to graph theory. A literally global motivating example to keep your head in the game once the going turns esoteric, as graph theory inevitably does.

Conversely, if you have no interest in graph theory, know that Kiss et al. have produced a surprisingly accessible introduction to epidemiology. (LabKitty loves me some Linda Allen, but -- let's face it -- she's not above the occasional Lebesgue integral.)

And if you are interested in both graph theory and epidemiology, then Kiss et al. is your jam. They begin with the basic SIR compartment model, extend it to include stochastic transitions, then introduce metrics of network geometry and its influence on disease spread. And that's just in chapter one. From there they consider exact propagation models, mean-field and PDE approximations, percolation models, adaptive networks, and more. An appendix addresses computational issues, which TBH is mostly just a collection of pseudocode. (Perhaps they might expanded on this in a second edition.)

The net result is a sum much more than the sum of its parts. Like peanut butter and chocolate, fire and gasoline, or incompetence and the presidency.

Read all about Epidemics on Networks on Amazon.