Pre-immunity: the Schrödinger’s cat of immunology

Abstract

AbstractEarly 2020, catastrophic consequences of COVID-19 was predicted in the do-nothing scenario, based on mathematical models for epidemiology. As data began to emerge, several scientists noted that growth did not seem exponential, as the models predicted, leading to speculations of pre-existing immunity or immunological dark matter to explain this pattern. On the other hand, reports of choir-rehearsals infecting most members seemed to refute this, and the topic remained inconclusive. We provide a mathematical theory in which both observations are true; on a population level, pre-immunity exists, on an individual level, it doesn’t. This theory demonstrates that established formulas relating e.g. R0 and the herd-immunity threshold are wrong. We derive new mathematical formulas, which applies to any virus whose transmission dynamics is associated with large individual variability in susceptibility to the infection. Contrary to great variability in infectivity, which we show has no bearing on the mathematical modeling, variability in susceptibility actually manifests itself as pre-immunity on a macroscopic scale, thus making pre-immunity a necessity for accurate mathematical modeling.