Model Based Estimation of the SARS-CoV-2 Immunization Level in Austria and Consequences for Herd Immunity Effects

Abstract

Several systemic factors indicate, that worldwide herd immunity against COVID-19 will probably not be achieved in 2021. Vaccination programs are limited by availability of doses, the number of people already infected is still too low to have a disease preventing impact and new emerging variants of the virus seem to partially neglect developed antibodies from previous infections. Nevertheless, after one year of COVID-19 observing high numbers of reported cases in most European countries, we might expect that the immunization level should have an impact on the spread of SARS-CoV-2. We used an agent-based simulation model to reproduce the COVID-19 pandemic in Austria to estimate the immunization level of the population as of February 2021. We ran several simulations of an uncontrolled epidemic wave with varying initial immunization scenarios to assess the effect on the effective reproduction number. We also used a classic differential equation SIR-model to cross-validate the simulation model. As of February 2021, 14.7% of the Austrian population has been affected by a SARS-CoV-2 infection which causes a 9% reduction of the effective reproduction number and a 24.7% reduction of the prevalence peak compared to a fully susceptible population. This estimation is now recomputed on a regular basis to publish model based analysis of immunization level in Austria also including the fast growing effects of vaccination programs. This provides substantial information for decision makers to evaluate the necessity of NPI-measures based on the estimated impact of natural and vaccinated immunization.

Longitudinal monitoring of SARS-CoV-2-specific immune responses

“…As the incidence of seroconversion of 23.6-25.0% was markedly higher at that time point as predicted from the positive PCR tests, our data hint towards a significantly higher prevalence of SARS-CoV-2 positive people in this Austrian hotspot than officially recorded. This high level of undetected cases is in line with other reports from Austria (31).…”

Robust models of disease heterogeneity and control, with application to the SARS-CoV-2 epidemic

“…Due to increases in the availability and use of COVID-testing in Austria, we use the following estimates for the detection ratio in 2021: 1/2.3 for January and February, 1/2 for March and 1/1.4 for April and beyond. These are consistent with model-based estimates for Austria which use hospitalizations and deaths to learn about the proportion of unreported infections [12,13].…”

“…We specify a detection ratio that an infected individual is diagnosed and appears in the official case statistics; this is important, because the controller responds to detected cases and our validation experiments compare to observed cases. In the application to Austrian data, we use a detection ratio of 1/1.4, which is informed by local models which consider estimates of IFR and use jointly the detected cases, hospitalizations, and deaths due to COVID-19 [12,13].…”

“…Here, we have ignored the small number of currently infected individuals by dividing by N instead of P h2H jS h j. Eq (12) provides a useful summary as an average effect implied by our model which accounts for variant heterogeneity, population diversity, and superspreading. Unfortunately, a controller cannot compute it as it depends on the unknown parameters θ h , which describe the "momentum" of the disease [1].…”

Estimation of Total Immunity to SARS-CoV-2 in Texas

“…People obtain immunity through either natural infection with SARS-CoV-2 or vaccination, and total immunity is the combination of these two avenues of immunity. Usually, an estimate of total immunity is obtained using mathematical modeling and simulation, which require inputs such as duration of immunity once infected, viral reproduction rate, population mixing, and additional factors [1,2,3,4,5]. However, the contributions of these inputs are still not fully known.…”