Effective Mathematical Modelling of Health Passes during a Pandemic

TL;DR

This paper develops mathematical models to evaluate the effectiveness of health passes in controlling COVID-19 spread, considering vaccination and testing, validated with data from European countries.

Contribution

It introduces a novel combination of compartmental and Renormalisation Group models to analyze health pass policies over an entire epidemic wave.

Findings

Health passes significantly reduce transmission when high vaccination coverage is achieved.

Model predictions align well with COVID-19 data from Germany and Austria.

Vaccination rate and coverage are critical factors in policy effectiveness.

Abstract

We study the impact on the epidemiological dynamics of a class of restrictive measures that are aimed at reducing the number of contacts of individuals who have a higher risk of being infected with a transmittable disease. Such measures are currently either implemented or at least discussed in numerous countries worldwide to ward off a potential new wave of COVID-19 across Europe. They come in the form of Health Passes (HP), which grant full access to public life only to individuals with a certificate that proves that they have either been fully vaccinated, have recovered from a previous infection or have recently tested negative to SARS-Cov-19 . We develop both a compartmental model as well as an epidemic Renormalisation Group approach, which is capable of describing the dynamics over a longer period of time, notably an entire epidemiological wave. Introducing different versions of HPs in this model, we are capable of providing quantitative estimates on the effectiveness of the underlying measures as a function of the fraction of the population that is vaccinated and the vaccination rate. We apply our models to the latest COVID-19 wave in several European countries, notably Germany and Austria, which validate our theoretical findings.