In constant parameter compartmental models an early onset of herd immunity is at odds with estimates of R values from early stage growth. In a bid to resolve this conundrum we are inspired by de Finetti's Theorem, and we exhibit equivalence classes of meta-population models that are orbits of the symmetric group. We illustrate with a mixture of stochastic SIR models in which growth can be inferred from a classic bond pricing formula of Vasicek. This approach exploits the symmetry of model observables, and then uses convexity adjustments to directly determine the degree of variation that is needed to locate the orbit of nature's model . Convexity adjustments are also useful, and material, for cross-sectional comparison. We consider some stylized population density profiles and derive easy to use rules of thumb for estimating threshold infection level in one region given knowledge of threshold infection in another.
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.
R
In a bid to resolve this conundrum we are inspired by
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,
R
and we exhibit equivalence classes of meta-population models that are orbits of the symmetric group. We illustrate with a mixture of stochastic SIR models in which growth can be inferred from a classic bond pricing formula of Vasicek. This approach exploits the symmetry of model observables, and then uses convexity adjustments to directly determine the degree of variation that is needed to locate the orbit of nature's model
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
R
are also useful, and material, for cross-sectional comparison. We consider some stylized population density profiles and
can also be used for cross sectional comparisons and we