The Rules of Contagion

May 15, 2020
A geeky but fascinating exploration of the mathematics of things that go viral--not least of them viruses. "If we want a better grasp of contagion, we need to account for its dynamic nature," writes Kucharski, who does mathematical modeling of disease transmission at the London School of Hygiene & Tropical Medicine. He elaborates throughout: Contagion is constantly in motion as it courses through a population, finding its "susceptibles" and slowing down as the number of susceptibles declines. By the author's capable account, the math works out pretty much the same whether applied to some negative force, such as a COVID-19 category virus or the concomitant financial crumbling that has surrounded it, or some positive force--e.g., a cultural innovation such as a pop song or dance move. Kucharski works his way through some key epidemiological ideas, including one advanced by the scientist who put it together that malaria was spread by mosquitos, earning him the Nobel Prize--although that scientist later protested that his larger achievement was formulating "general laws of epidemics." These laws embody a mathematical formula that looks rather like an hourglass turned on its side, representing three key groups: the susceptible, the infectious, and the recovered. There are also the dead, of course, but they don't move, as the dynamic model does. Kucharski takes his readers down provocative detours, such as the use of public-health models of disease transmission to examine how social networks figure in urban gun violence, with algorithms that take into account such things as "age gang affiliations, and prior arrests." When things go viral, all kinds of interesting mathematical and real-world effects can happen, from stock market bubbles to horrific explosions of disease. Kucharski is there, calculator in hand, to suss it all out, and highly numerate readers will enjoy going along with the ride to guesstimate the R value of a contagion's spread. Utterly timely and readable, if not terribly comforting in the midst of the current pandemic.

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