  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.
