Addressing the Herd Immunity Paradox Using Symmetry, Convexity Adjustments and Bond Prices

TL;DR

This paper explains the apparent early herd immunity onset discrepancy in epidemiological models by applying interest rate bond pricing and convexity adjustments, offering a novel perspective without seeking a true model but an equivalent one.

Contribution

It introduces a novel approach combining interest rate modeling and statistical symmetry to reconcile differences in epidemiological model predictions.

Findings

Convexity formulas reduce model prediction discrepancies.

Bond pricing formulas explain herd immunity paradox.

Rules of thumb for cross-regional infection thresholds.

Abstract

In constant parameter compartmental models an early onset of herd immunity is at odds with estimates of R values from early stage growth. This paper utilizes a result from the theory of interest rate modeling, namely a bond pricing formula of Vasicek, and an approach inspired by a foundational result in statistics, de Finetti's Theorem, to show how the modeling discrepancy can be explained. Moreover the difference between predictions of classic constant parameter epidemiological models and those with variation and stochastic evolution can be reduced to simple "convexity" formulas. A novel feature of this approach is that we do not attempt to locate a true model but only a model that is equivalent after permutations. Convexity adjustments can also be used for cross sectional comparisons and we derive easy to use rules of thumb for estimating threshold infection level in one region given knowledge of threshold infection in another.