Papers

Peter Cotton's papers and notes on epidemics. Shorter pieces are under Essays.

Preprints

Cotton, P. (2020). Repeat Contacts and the Spread of Disease: An Agent Model with Compartmental Solution. Preprint. arXiv:2005.10311. SIR with transmission attenuated by the probability that a contact is new, derived from agents moving in the plane. How fast acquaintances go stale changes final sizes by an order of magnitude.
Cotton, P. (2020). Addressing the Herd Immunity Paradox Using Symmetry, Convexity Adjustments and Bond Prices. Preprint. arXiv:2006.07341. The growth convexity from the moment generating function of the transmission rate, or Vasicek's bond formula for an Ornstein–Uhlenbeck rate, and the harmonic-mean convexity at the peak. Summarized on mixtures and convexity.

Cotton, P. (2026). The Immunity Factor from Contact Surveys: Where Epidemics Turn Over. Working paper. PDF · TeX · code and log. The effective reproduction number falls approximately as $R S^\lambda$. Repeated UK contact surveys, under a model of persistent and changing activity, predict $\lambda = 4.6$-$5.2$ with daily contacts capped at 50 and 3.4-3.7 at 20, without fitting to epidemic outcomes; winter US county waves imply 2.4-5.3 over fatality rates from 0.5% to 1%. Where contacts were cut, first waves peaked with 1-5% infected.