Swiss public health measures associated with reduced SARS-CoV-2 transmission using genome data

Genome sequences from evolving infectious pathogens allow quantification of case introductions and local transmission dynamics. We sequenced 11,357 severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) genomes from Switzerland in 2020 - the sixth largest effort globally. Using a representative subset of these data, we estimated viral introductions to Switzerland and their persistence over the course of 2020. We contrasted these estimates with simple null models representing the absence of certain public health measures. We show that Switzerland’s border closures de-coupled case introductions from incidence in neighboring countries. Under a simple model, we estimate an 86–98% reduction in introductions during Switzerland’s strictest border closures. Furthermore, the Swiss 2020 partial lockdown roughly halved the time for sampled introductions to die out. Last, we quantified local transmission dynamics once introductions into Switzerland occurred, using a phylodynamic model. We found that transmission slowed 35–63% upon outbreak detection in summer 2020, but not in fall. This finding may indicate successful contact tracing over summer before overburdening in fall. The study highlights the added value of genome sequencing data for understanding transmission dynamics.


S2: New Zealand validation data
For New Zealand, the sequence submitters provided additional information on which samples were from cases in managed isolation and quarantine (MIQ) facilities versus the broader community. This allows us to partially evaluate our introduction identification methods. 117 of the 1234 analyzed focal sequences in the New Zealand analysis originated from MIQ facilities. 63 (54%) of these were singletons under the "many introductions'' polytomy assumption versus 37 (32%) under the "few introductions" assumption. 44 (38%) or 37 (32%) were plausible within-MIQ outbreaks. These were identified as introductions with cases all from a single region and all MIQ. They may represent groups of individuals quarantining together or infected in the same source location. These outbreaks included, on average, 3 samples spanning 5 days (many introductions) or 2 samples spanning 9 days (few introductions). The remaining 10 (9%) or 43 (37%) of MIQ sequences were in introductions including community cases or including cases in multiple MIQ facilities in different regions, which we deem unrealistic. These results support that the "many introductions" polytomy assumption is more realistic when the probability of infection abroad is high compared to the probability of locally acquired infection.

S3: Sensitivity analyses for phylodynamic modeling
Here we describe a sensitivity analysis and some example intermediate outputs from our phylodynamic analysis.
Sampling proportion prior. We repeated our analyses using two different priors on the sampling proportion. The first, unbounded prior was LogUniform(10 −4 , 1). This broad prior allows the sampling proportion to assume any value. The second, bounded prior was LogUniform(10 −4 , 0.05). This narrower prior is motivated by our 5% down-sampling based on confirmed case numbers. Figure S7A shows that in Switzerland, the estimated sampling proportion in late fall 2020 varies greatly depending on the prior. The rise in prevalence of lineage B.1.177 during this period (29), representing a drop in SARS-CoV-2 diversity in Switzerland, might explain why the inference under the broader sampling prior estimates a proportion corresponding to fewer individuals than we know were infected during this time. Figure S7B shows that the effective reproductive number estimates in fall 2020 for Switzerland more closely match estimates based on confirmed case data when the sampling proportion is treated as a fitting parameter, that is, under the first, broad prior. Therefore, we report results under this prior in the main text. In Figure S8A, we show that the damping factor results are qualitatively similar between the two sampling proportion priors. For the New Zealand analysis, Re-estimates are not affected by bounding the sampling proportion or not ( Figure S10).
Logged trees. We visually inspected phylogenetic trees for a few introductions. These trees were sampled and logged by the Markov chains in the phylodynamic analyses. Note that the damping factor results are jointly inferred from all the branching events across introductions in each time period. For each set of model assumptions and each month, we inspected maximum clade credibility summary trees for the 50th and 95th percentile largest introductions that were first sampled that month and eventually yielded >2 samples. Figure  S9 shows as an example summary trees for these introductions from one of the MCMC chains in the phylodynamic analysis for Switzerland with damping factors and an unbounded sampling proportion prior.

S4: BDSKY introduction correction and damping factor extension
First we describe the correction applied to the number of observed introductions each week based on the BDSKY model. Then we describe the implementation of an extension to the BDSKY model to incorporate a transmission damping factor.
Correction to the number of observed introductions. The correction described here is to account for the time-varying Re in Switzerland, which affects the probability a new introduction each week went un-sampled through the end of the sampling period. The equations are taken from (16).
Let the birth rate change weekly at times ( = 1, … , − 1), where the process ends at time (the end of the sampling period). The death rate and sampling rate are assumed to be constant through time. Let and be convenience parameters to simplify notation. They are defined as follows: where ( ) is the probability that an infected individual at time has no sampled descendants when the process ends. It is defined as follows: In pseudocode, ( ) is calculated for each weekly change time as follows: 1. Calculate for each time period . 2. Calculate using +1 ( ) = 1 since the probability an infected individual at time having no sampled descendants is 1. 3. For ( = , … , 1), calculate first and then −1 ( ).
Last, the number of observed introductions each week , is corrected for the probability a new introduction at the start of that week went un-sampled through the end of the sampling period: = , 1 − Implementation of the transmission damping factor. This section describes the implementation of a "damping factor" extension to the parameterization of the BDSKY phylodynamic model presented in (16).
As described in the main text, the damping factor is a multiplicative factor applied to the birth rate two days after the first sample in each identified introduction was collected. The value of the damping factor applied to each introduction is allowed to change at two times (representing the start of summer and start of fall).
This parameter configuration is an input to the new BEAST2 parameterization "EpiParameterizationMod", available at https://doi.org/10.5281/zenodo.7258644. The probability density of each sampled tree is identical to that presented in Stadler et al. 2013 where the piecewise-constant birth rate of a tree is modulated by the appropriate damping factor beginning two days after the first sample.     (22). The null model is fit to the points prior to the border closure on 13 March (highlighted with shaded rectangle), values after that are a model prediction. Uncertainty bounds for total introductions (error bars) and null model predictions (colored shaded areas) are based on the 95% upper and lower HPD bounds for Re when estimating total introductions. The orange and green colors correspond to estimates generated under our few and many introductions polytomy assumptions, respectively.

Fig. S6. Heatmap of new introductions into Switzerland and their persistence by month.
Diagonal entries are the number of newly sampled introductions in Switzerland each month and off-diagonal entries are the number continuing to persist into each following month.
Introductions are counted once in the month they are first sampled ("Month of first sampling") and one every following month ("Month of ongoing sampling") until the date of the latest sample. Estimates were generated under two different polytomy assumptions giving rise to either few or many introductions. Ranges are: few-many.  (28) in gray. Additionally, Re estimates from the models with a damping factor (pink) are the "baseline" Re before introductionspecific damping (i.e., before application of a damping factor once introductions are older than 2-days post sampling).    (28) in gray. Additionally, Re estimates from the models with a damping factor (pink) are the "baseline" Re before introduction-specific damping (i.e. before application of a damping factor once introductions are older than 2-days post sampling).  Table S3. Sampling proportion change-points for the phylodynamic analysis on Swiss data. The sampling proportion was modeled as a piecewise-constant function in time, with the following change-points motivated by major shifts in the testing regime or genome sequencing intensity in Switzerland.