Heterogeneity and Superspreading Effect on Herd Immunity

TL;DR

This paper models how heterogeneity and superspreading influence herd immunity thresholds, showing that these factors cause the effective reproduction number to decline faster, affecting the estimated infected population needed for herd immunity.

Contribution

It introduces a model accounting for heterogeneity and correlation in infectiousness and susceptibility, providing new insights into herd immunity thresholds and disease spread dynamics.

Findings

Heterogeneity accelerates the decline of the effective reproduction number.

The final infected population can be significantly larger than the herd immunity threshold.

Lock-down scenarios impact the ultimate size of the infected population.

Abstract

We model and calculate the fraction of infected population necessary to reach herd immunity, taking into account the heterogeneity in infectiousness and susceptibility, as well as the correlation between those two parameters. We show that these cause the effective reproduction number to decrease more rapidly, and consequently have a drastic effect on the estimate of the necessary percentage of the population that has to contract the disease for herd immunity to be reached. We quantify the difference between the size of the infected population when the effective reproduction number decreases below 1 vs. the ultimate fraction of population that had contracted the disease. This sheds light on an important distinction between herd immunity and the end of the disease and highlights the importance of limiting the spread of the disease even if we plan to naturally reach herd immunity. We analyze the effect of various lock-down scenarios on the resulting final fraction of infected population. We discuss implications to COVID-19 and other pandemics and compare our theoretical results to population-based simulations. We consider the dependence of the disease spread on the architecture of the infectiousness graph and analyze different graph architectures and the limitations of the graph models.