Population Susceptibility Variation and Its Effect on Contagion Dynamics

TL;DR

This paper introduces a mathematical framework to analyze how individual susceptibility variation influences contagion dynamics and herd immunity thresholds, highlighting the importance of accounting for susceptibility diversity in public health strategies.

Contribution

It develops new methods to explicitly incorporate susceptibility variation into contagion models, deriving formulas for herd immunity thresholds based on initial susceptibility distributions.

Findings

Ignoring susceptibility diversity overestimates herd immunity thresholds

Susceptibility variation significantly impacts contagion outcomes

Mathematical tools enable better public health intervention planning

Abstract

Susceptibility governs the dynamics of contagion. The classical SIR model is one of the simplest compartmental models of contagion spread, assuming a single shared susceptibility level. However, variation in susceptibility over a population can fundamentally affect the dynamics of contagion and thus the ultimate outcome of a pandemic. We develop mathematical machinery which explicitly considers susceptibility variation, illuminates how the susceptibility distribution is sculpted by contagion, and thence how such variation affects the SIR differential questions that govern contagion. Our methods allow us to derive closed form expressions for herd immunity thresholds as a function of initial susceptibility distributions and suggests an intuitively satisfying approach to inoculation when only a fraction of the population is accessible to such intervention. Of particular interest, if we assume static susceptibility of individuals in the susceptible pool, ignoring susceptibility diversity {\em always} results in overestimation of the herd immunity threshold and that difference can be dramatic. Therefore, we should develop robust measures of susceptibility variation as part of public health strategies for handling pandemics.