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Summary

Results

Three recently detected variants (B.1.1.7, B.1.351, P.1) of SARS-CoV-2 have been detected in various countries worldwide including Switzerland. We aim at tracking the spread of these variants in the cantons of Geneva, Bern, and Zurich, and in Switzerland overall. As a comparison, we also provide an analysis of the spread of B.1.1.7 in Denmark. Finally, we estimate the current proportion of the variants for a given region and their increased transmissibility.

Figure 1. Increase in the proportion of SARS-CoV-2 variants among positive samples in Switzerland and Denmark. Note that the projected trajectories for Zurich and Switzerland are overlapping. Error bars and shaded areas correspond to 95% confidence intervals of the data (blue) and model (red), respectively.

The proportion of the variants has increased rapidly in all regions (Figure 1). Fitting a logistic growth model to the data allows to quantify and project the increase in the proportion of the new variants (see Methods) (Figure 2, Table 1). Note that due to the delay from infection to sample collection, the shown increase and the estimated proportions of the new variants reflect the epidemic situation from around one week ago.

Figure 2. Estimated proportion of the variant (left) and increase in transmissibility (right). The increase in transmissibility is estimated assuming the effective reproduction number of the wild-type \(R_w \approx 1\) and an exponentially (blue) and delta (green) distributed generation time of 5.2 days (Ganyani et al.). Error bars correspond to 95% confidence intervals.

Table 1. Estimated proportion of the variant and increase in transmissibility. The increase in transmissibility is estimated assuming the effective reproduction number of the wild-type \(R_w \approx 1\) and an exponentially (blue) and delta (green) distributed generation time of 5.2 days (Ganyani et al.).

Region Variant Proportion at 5 Mar 2021 Increase in transmissibility
Geneva 501Y 91% (89%-93%) 38% (34%-43%) - 47% (40%-53%)
Bern 501Y 74% (66%-80%) 41% (35%-48%) - 51% (42%-62%)
Zurich 501Y 78% (72%-82%) 40% (36%-45%) - 50% (43%-57%)
Switzerland B.1.1.7 78% (75%-81%) 45% (42%-47%) - 56% (53%-60%)
Denmark B.1.1.7 86% (85%-87%) 46% (45%-47%) - 58% (56%-60%)

The estimates for the increase in transmissibility are in good agreement with earlier findings for B.1.1.7 in the UK and other countries (Volz et al., Davies et al., Leung et al.). Taken together, these findings underline the importance of efficient control measures in order to prevent an increase in SARS-CoV-2 incidence in Switzerland.

Methods

Data

We use data sets from the following five regions for our analysis (download here):

Model

Competitive growth between variant and non-variant (‘wild-type’) strains of SARS-CoV-2 can be described by the following two ordinary differential equations: \[\begin{align} \frac{dW}{dt} &= \beta S W - \gamma W, \\ \frac{dV}{dt} &= \beta (1 + \tau) S V - \gamma V, \end{align}\] where \(W\) and \(V\) are individuals infected with wild-type and variant, respectively, and \(S\) the population of susceptibles. For the variant, the transmission rate \(\beta\) is increased by the factor \(1 + \tau\) and both strains are cleared at rate \(\gamma\). For \(\tau > 0\), one can easily show that the proportion of the new variant among all infections increases according to logistic growth: \[\begin{align} p(t) &= \frac{V(t)}{W(t) + V(t)} = \frac{1}{1 + \kappa e^{- \rho t}}, \end{align}\] where \(\kappa = W(0)/V0\) and \(\rho = \beta \tau S\), i.e., the difference in the net growth rates between the variant and the wild-type. \(\rho\) can be directly estimated by fitting a logistic growth model (binomial regression) to the proportion of the new variant. The increased transmissibility of the variant is then given by \(\tau = \rho/(\beta S)\). Since the effective reproduction number of the wild-type is \(R_w = \beta S/\gamma\) and the generation time is \(D = 1/\gamma\), we obtain \(\tau = \rho D/R_w\). For a situation where \(R_w \approx 1\), we can simplify to \(\tau \approx \rho D\). This derivation assumes an exponentially distributed generation time. For a delta distributed generation time, one finds that \(\tau \approx e^{\rho D} - 1\).

Funding