Essays

Shorter pieces by Peter Cotton, written as the 2020 epidemic unfolded, where the herd-immunity paradox and its convexity explanation first appeared.

• Cotton, P. (2020). A Fundamental Theorem for Epidemiology. Article, 27 May 2020. Doubling times under a week against peak infection near 20%: de Finetti's theorem reduces the question to mixtures of independent neighbourhoods, and the susceptible share at the peak to a harmonic mean.
• Cotton, P. (2020). How Population Shape Tilts Your Odds of Getting COVID-19. Article. When contagiousness varies with population density, Jensen's inequality lowers the herd-immunity threshold through a harmonic mean, with a closed form when contagiousness is a power of density.
• Cotton, P. (2020). Got Milk? On Homogenization and Survival Probability. Article. Survival under a hazard rate that switches between regimes, with infection risk for commuters as the opening example; the mathematics is developed at homogenization.microprediction.org.

More essays, on prediction, markets and statistics, are on Medium.