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Structural features and the heterogeneity of disease transmissions play an essential role in the dynamics of epidemic spread. But these aspects can not completely be assessed from aggregate data or macroscopic indicators such as the effective reproduction number. We propose an index of effective aggregate dispersion (EffDI) that indicates the significance of infection clusters and superspreading events in the progression of outbreaks by carefully measuring the level of stochasticity in time series of reported case numbers. This allows to detect the transition from predominantly clustered spreading to a diffusive regime with diminishing significance of singular clusters, which can be decisive for the future progression of outbreaks and relevant in the planning of containment measures. We evaluate EffDI for SARS-CoV-2 case data in different countries and compare the results with a quantifier for the socio-demographic heterogeneity in disease transmissions in a case study to substantiate that EffDI qualifies as a measure for the heterogeneity in transmission dynamics.

Several systemic factors indicate that worldwide herd immunity against COVID-19 will probably not be achieved in 2021. On the one hand, vaccination programs are limited by availability of doses and on the other hand, 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, by February 2021 after one year of observing high numbers of reported COVID-19 cases in most European countries, we might expect that the immunization level should have an impact on the spread of SARS-CoV-2. Here we present an approach for estimating the immunization of the Austrian population and discuss potential consequences on herd immunity effects. To estimate immunization we use a calibrated agent-based simulation model that reproduces the actual COVID-19 pandemic in Austria. From the resulting synthetic individual-based data we can extract the number of immunized persons. We then extrapolate the progression of the epidemic by varying the obtained level of immunization in simulations of an hypothetical uncontrolled epidemic wave indicating potential effects on the effective reproduction number. We compared our theoretical findings with results derived from a classic differential equation SIR-model. As of February 2021, $$14.7\%$$ 14.7 % of the Austrian population has been affected by a SARS-CoV-2 infection which causes a $$9\%$$ 9 % reduction of the effective reproduction number and a $$24.7\%$$ 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 non pharmaceutical intervention measures based on the estimated impact of natural and vaccinated immunization.

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.