COVID-19 Modeling Outcome versus Reality in Sweden

Abstract

It has been very difficult to predict the development of the COVID-19 pandemic based on mathematical models for the spread of infectious diseases, and due to major non-pharmacological interventions (NPIs), it is still unclear to what extent the models would have fit reality in a "do nothing" scenario. To shed light on this question, the case of Sweden during the time frame from autumn 2020 to spring 2021 is particularly interesting, since the NPIs were relatively minor and only marginally updated. We found that state of the art models are significantly overestimating the spread, unless we assume that social interactions significantly decrease continuously throughout the time frame, in a way that does not correlate well with Google-mobility data nor updates to the NPIs or public holidays. This leads to the question of whether modern SEIR-type mathematical models are unsuitable for modeling the spread of SARS-CoV-2 in the human population, or whether some particular feature of SARS-CoV-2 dampened the spread. We show that, by assuming a certain level of pre-immunity to SARS-CoV-2, we obtain an almost perfect data-fit, and discuss what factors could cause pre-immunity in the mathematical models. In this scenario, a form of herd-immunity under the given restrictions was reached twice (first against the Wuhan-strain and then against the alpha-strain), and the ultimate decline in cases was due to depletion of susceptibles rather than the vaccination campaign.

Keywords: COVID-19; SARS-CoV-2; SEIR; SIR; modeling.

Figure A1

Fraction vaccinated v as function of time t.

Figure 1

Full data series (weekly average) from the Swedish Public Health Agency. During first wave, only patients admitted to hospital were tested, so the data are very unreliable. General testing started in late May 2020. The red section indicates the time frame we focus on in this paper.

Figure 2

(Left): 7-day rolling average of new cases in Stockholm county, adjusted to match the reported increase in seroprevalence of antibodies against SARS-CoV-2. The numbers 1–5 correspond with the updates to the NPIs in Table 1. (Right): total cases separated in Wuhan-strain and Alpha-strain.

Figure 3

Comparison between real data and model outcome for the age-stratified SEIR and age-activity-stratified SEIR based on [5], which assumes that contact patterns are stable over time. The pink graph is produced with variable social interactions (over time), as described further in Section 4.1.

Figure 4

(Left): relative change in daily contacts needed to obtain a good fit with real data. The green area accounts for uncertainty about how much more contagious the alpha-strain was. The red central curve assumes 50% more contagious (following [16]), and the (almost perfect) data fit in Figure 3 (pink curve) is computed based on this. (Right): actual reduction in mobility pattern according to Google Mobility Data. Notice that the y-axis is the same in both the left and the right image, and that one would expect to see similar curves given that Hypothesis 1 holds.

Figure 5

Google-mobility data over the full pandemic time-frame, preprocessed as in Figure 4.

Figure 6

Actual and modeled curves using artificial pre-immunity. The brown-orange, yellow, and blue curves display measured cases, separated into Wuhan-strain, alpha-strain, and total, respectively, same as in Figure 2 (so reweighted as before). The green, light-blue, and dashed black display corresponding curves for our model. Finally, the pink dashed curve shows total model output in the absence of vaccinations (only displayed during April–May 2021). Clearly, if this model is correct, the vaccination campaign had virtually no part in the final demise during May 2021, contrary to popular belief.