Extended compartmental model for modeling COVID-19 epidemic in Slovenia

Abstract

In the absence of a systematic approach to epidemiological modeling in Slovenia, various isolated mathematical epidemiological models emerged shortly after the outbreak of the COVID-19 epidemic. We present an epidemiological model adapted to the COVID-19 situation in Slovenia. The standard SEIR model was extended to distinguish between age groups, symptomatic or asymptomatic disease progression, and vaccinated or unvaccinated populations. Evaluation of the model forecasts for 2021 showed the expected behavior of epidemiological modeling: our model adequately predicts the situation up to 4 weeks in advance; the changes in epidemiologic dynamics due to the emergence of a new viral variant in the population or the introduction of new interventions cannot be predicted by the model, but when the new situation is incorporated into the model, the forecasts are again reliable. Comparison with ensemble forecasts for 2022 within the European Covid-19 Forecast Hub showed better performance of our model, which can be explained by a model architecture better adapted to the situation in Slovenia, in particular a refined structure for vaccination, and better parameter tuning enabled by the more comprehensive data for Slovenia. Our model proved to be flexible, agile, and, despite the limitations of its compartmental structure, heterogeneous enough to provide reasonable and prompt short-term forecasts and possible scenarios for various public health strategies. The model has been fully operational on a daily basis since April 2020, served as one of the models for decision-making during the COVID-19 epidemic in Slovenia, and is part of the European Covid-19 Forecast Hub.

Figure 1

Scheme of the extended SEIR model with additional compartments to model asymptomatic and symptomatic cases with hospital and ICU admissions, split into two separate submodels to model vaccinated and unvaccinated populations.

Figure 2

Scheme of the group-stratified extended SEIR model obtained by cloning the base model from Fig. 1, which allows for weighted and time-dependent population mixing between groups. The concept was used to model five population age groups.

Figure 3

COVID-19 epidemic situation in Slovenia in years 2021 (a) and 2022 (b). Weekly incidence of confirmed COVID-19 cases (black) and the proportion of population vaccinated against COVID-19 with the first (red), the second (yellow), and the booster dose (blue)^,,, are shown. The phases of the epidemic, together with prevailing viral variants and non-pharmaceutical public health interventions, are briefly described in the timeline on top.

Figure 4

Model forecasts of weekly incidence of COVID-19 confirmed cases. Black dots represent actual data. The colored dots represent predictions for 1, 2, 3 and 4 weeks ahead, the colored areas represent their confidence intervals. Forecasts from the same date are represented with the same color.

Figure 5

Model forecasts of weekly incidence of COVID-19 hospital admissions. The representation is the same as in Fig. 4.

Figure 6

Model forecasts of weekly incidence of deaths due to COVID-19. The representation is the same as in Fig. 4.