Herd immunity under individual variation and reinfection

TL;DR

This paper analyzes a SEIR epidemic model with individual variation in susceptibility and exposure, deriving explicit formulas for herd immunity thresholds that are lower than in homogeneous populations, and explores model extensions.

Contribution

It provides explicit formulas for herd immunity thresholds in heterogeneous populations and extends the existing SEIR model to account for individual variation.

Findings

Herd immunity threshold is lower with individual variation.

Explicit formulas for herd immunity thresholds are derived.

Model extensions explore additional heterogeneity factors.

Abstract

We study a SEIR model considered by Gomes et al. \cite{Gomes2020} and Aguas et al. \cite{Aguas2020} where different individuals are assumed to have different levels of susceptibility or exposure to infection. Under this heterogeneity assumption, epidemic growth is effectively suppressed when the percentage of population having acquired immunity surpasses a critical level - the herd immunity threshold - that is lower than in homogeneous populations. We find explicit formulas to calculate herd immunity thresholds and stable configuration, and explore extensions of the model.