Model fit to hospitalization data

We fitted our model to weekly hospitalization counts of Swedish and Norwegian regions from February 21, 2020 to July 29, 2021, accounting for age-prioritized vaccination roll-out in the beginning of 2021. Estimation was performed in a Bayesian framework using Hamiltonian Monte Carlo in a custom implementation of the model in Stan [14] using the CmdStanR interface [15]. Detailed information on the definition of the region-level extended SIR model, the likelihood for the weekly hospitalization counts, as well as the fixed parameters and priors for the estimated parameters can be found in the Materials and Methods section. We fitted two separate models, one for joint modeling of the 11 Norwegian regions (fylke) and one for the 21 regions (län) of Sweden.

Visual investigation of trace plots indicated convergence of the four independent MCMC chains per model to a joint posterior distribution, the convergence diagnostic provided by Stan was smaller than 1.01 for all sampled parameters providing no evidence for convergence problems [16]. Fig 1 shows that our highly flexible model is able to capture the development of weekly hospitalization counts well, visualized based on the examples of Oslo in Norway and Stockholm in Sweden. Panel A illustrates the model fit, Panel B shows the estimated effective reproduction number and Panel C the contribution of the different GMCR categories over time. The flexibility of the model stems from the large amount of parameters that are estimated, in particular the region specific weekly number of secondary infection not captured in the GCMR setting, . Fig. 26 - Fig. 31 in S1 Appendix provide similar plots for each Norwegian and Swedish region.

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Fig 1. Model fit for two selected regions, Oslo and Stockholm.

Panel A shows the weekly hospitalization counts: Oslo and Stockholm (green dots) as well as the model based expected hospitalization counts and associated 90%-credible interval. Panel B shows the estimated time-varying reproduction number, which is a function of the estimated and corresponds to the expected number of secondary contacts per infected at each time-point and an associated 90%-credible interval. Panel C shows the model-based time-varying contribution of each transmission setting of the considered COVID-19 community mobility reports to these secondary infections.

https://doi.org/10.1371/journal.pgph.0006368.g001

In addition to changes in contact frequencies represented via the additive model for the GCMR, our model of SARS-CoV-2 transmissibility accounts for multiplicative changes in infection risk per contact associated with the Alpha and Delta variants of concern (VoC) and seasonal effects. We assume that these multiplicative effects are the same in all regions considered in the respective model (Sweden or Norway), and our estimates from the data of the Norwegian and Swedish regions are quite similar, as shown in Fig 2. We estimate that an increase in temperature of 20 degree Celsius (corresponding approximately to the difference between the average temperature of the coldest winter and warmest summer month) leads to a reduction in transmissibility by around 40%. Note that the median difference between the mean temperature in the warmest and coldest month of the year per region is 20.4 degrees in our observation period. For the Alpha VoC, we estimated an increase in transmissibility compared to the wild-type of around 20% based on data of the Norwegian regions but found no clear evidence for an increase in transmissibility in the Swedish data. For the Delta VoC, we estimated approximately a doubling of transmissibility compared to the wild-type in both Norway and Sweden, albeit with substantial uncertainty.

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Fig 2. Multiplicative effects on transmission probability.

Shown are the estimated posterior median and 90%-credible intervals for the multiplicative effects of VoC’s and a 20-degree temperature difference on the transmissibility for the Norwegian (red) and Swedish (blue) regions, respectively.

https://doi.org/10.1371/journal.pgph.0006368.g002

Activity at Transit stations and Workplaces capture most important settings of infection in Norway and Sweden

Based on the estimated parameters from our model, contacts in settings captured by the Transit and Workplaces categories lead to most infections at the usual pre-pandemic activity: the point estimate for the Transit was highest in 7 out of 11 Norwegian regions and in 9 out of 22 Swedish regions. In the remaining 4 regions in Norway and in 11 of the 12 remaining regions in Sweden the Workplace category was most important (see Table 3 in S1 Appendix). Fig 3 shows the population-weighted average of the relative share of secondary infections assigned to each setting at baseline activity. If activity stayed unchanged, we estimate most infectious contacts captured by activity at the Transit setting, followed by Workplaces, Retail & recreation, and lastly Grocery & pharmacies for Norway and Sweden. The posterior probability that the population-weighted mean of the Transit category is largest among the four categories is 0.55 for Norway and 0.68 for Sweden. Furthermore, we estimated a posterior probability of 0.50 and 0.62 that the Transit and Workplace categories make up the settings with the largest contribution to transmission among the six two-setting combinations at baseline activity.

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Fig 3. Population-weighted relative contribution of the community mobility reports at BL activity.

Shown are the posterior median and 90%-credible intervals for the population-weighted relative contribution of each GCMR setting at baseline activity for Norway and Sweden.

https://doi.org/10.1371/journal.pgph.0006368.g003

Model attributed 60% of all infections to contacts in four GCMR settings for Sweden and 39% for Norway

Taking into account observed changes in activity in the GCMR categories, we derived the total share of infections that were attributed to contacts in settings captured by the four GCMR categories per country and for each county (see the Materials and Methods section). Aggregated over the whole time period and all counties, our model allocated 60.0% (90%-CI: 57.1-62.5%) of all infections in Sweden and 38.7% (33.2 - 43.8%) of all infections in Norway to settings captured by the GCMRs (Fig. 32 in S1 Appendix). The remaining, unexplained, infectious contacts were accounted for by the region-specific weekly parameters . Among the GCMR categories, settings captured by the Transit category still played the largest role when taking into account changes in activity over time (with 10.9% of all infections in Norway and 18.9% in Sweden). Differences in the share of infections between the categories were, however, less pronounced compared to the expected share of infections at baseline activity: the relative contribution of contacts captured by the Work category decreased, and the importance of contacts captured by the Retail and recreation category increased (Table 5 in S1 Appendix).

When investigating how much of the SARS-CoV-2 transmission dynamics was explained by the GCMRs in each county overall and per category, we found rather large differences. The mean share of daily infectious contacts in settings captured by the GCMRs varied between 27.5% and 73.3%, the total share of infections assigned to the settings captured by the GCMRs was in a similar range, albeit slightly smaller for most regions (Fig. 32, Table 6 and Table 7 in S1 Appendix).

The GCMRs captured a larger share of infectious contacts in Swedish compared to Norwegian counties. We also observed a tendency towards a larger explanatory power for regions with higher population density. However, this correlation is rather weak and to a large extent driven by the capitals, Oslo and Stockholm, with high population density (Fig. 34 in S1 Appendix).

German regions

Our proposed model to describe the relationship between GCMRs and SARS-CoV-2 transmission rate, is not specific to Norway and Sweden, nor to the time period analyzed above. We estimated the model for two different regions from Germany, Bavaria and Berlin, in a shorter period (Feb 2020 - Dec 2020) based on publicly available data. For this period, no relevant virus variants or vaccination activity had to be considered (for more details, see the Materials and Methods section).

Fig 4 shows the model fit, estimated effective reproduction number and the contribution of the different GCMR categories for Bavaria and Berlin. Compared to the results in the Norwegian and Swedish regions, the GCMR activity categories captured a relatively large share of infectious contacts (64.5% in Bavaria, 69.7% in Berlin on a daily average). During the observation period, 65.2% (90%-CI: 58.7-69.9%) of all infections in Berlin and Bavaria were allocated to contacts in settings captured by the GCMRs. The multiplicative effect of the temperature on the disease transmission in Germany had a similar order of magnitude compared to Sweden and Norway: a 20 degree increase in temperature reduced the model-based transmission probability per contact by factor 0.50 (90%-CI: 0.44-0.59). The largest difference compared to the results in Sweden and Norway was the model-based relative contribution of the different GCMR categories to transmission, both at baseline activity and aggregated over the analysis period. In both German regions, and in particular Berlin, we estimated that activity in settings captured by the Retail & recreation category contributed most to infectious contacts at baseline activity, but also accounting for changes in activity over the observation period. It is followed by the Transit category, which instead was most important for Sweden and Norway (Fig. 5 in current text and Table 9 in S1 Appendix).

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Fig 4. Model fit for the two German regions, Bavaria and Berlin.

Panel A shows the weekly hospitalization counts: Bavaria and Berlin (green dots) as well as the model based expected hospitalization counts and associated 90%-credible interval. Panel B shows the estimated time-varying reproduction number, which is a function of the estimated and corresponds to the expected number of secondary contacts per infected at each time-point and an associated 90%-credible interval. Panel C shows the model-based time-varying contribution of each transmission setting of the considered COVID-19 community mobility reports to these secondary infections.

https://doi.org/10.1371/journal.pgph.0006368.g004

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Fig 5. Relative contribution of the community mobility reports at BL activity, Bavaria and Berlin.

Shown are the posterior median and 90%-credible intervals for the relative contribution of GCMR setting to the transmissibility at baseline activity, for the two analyzed German regions Bavaria and Berlin.

https://doi.org/10.1371/journal.pgph.0006368.g005

Sensitivity analysis for Germany

Our investigation of collinearity between the categories of the GCMR showed that for the German regions, the Transit stations setting was highly correlated with both the Retail and recreation setting and the Workplaces setting (Fig. 9 in S1 Appendix). Further investigation of multicollinearity between the categories, by the use of Condition Index (ref to litteratur), showed moderate to strong multicollinearity between the four categories Grocery and Pharmacy, Retail and Recreation, Transit stations and Workplaces. Excluding the Transit stations setting reduced this multicollinearity for both regions (Fig. 13 in S1 Appendix).

We performed a sensitivity analysis for the German regions, by removing the Transit station setting from the analysis. The model fit to hospitalizations remain good, see Fig 35 in S1 Appendix. After removing the Transit stations setting, the relative contribution of each setting to the transmissibility at baseline activity increases, with the biggest increase for the Retail and recreation setting (Table 11 and Fig. 36 in S1 Appendix). The estimated coefficients increases for each setting when removing Transit stations (Table 10 in S1 Appendix). The estimated share of the secondary infections attributed GCMR categories increases when removing the transit setting (Table 12 and Fig. 37 in S1 Appendix). Even though the contribution of each setting to different effect measures increases when removing the Transit stations setting, the differences are not big and the credible intervals do not indicate any significant difference in the results of the main analysis and the sensitivity analysis.

Google community mobility reports (GCMR)

Google provides a freely available data source, the Google COVID-19 Community Mobility Reports, a daily, region specific, activity level in different social settings [7]. These data are based on tracking Google users, who have “Location History” enabled on their mobile devices. Geographic locations are classified into six settings: Grocery and pharmacy, Retail and recreation, Transit stations, Parks, Workplaces, and Residential areas. For the first four settings, the GCMR index measures the percentage increase/decrease in the daily number of visits at locations classified to each setting, relative to a pre-pandemic baseline level. The baseline level, one for each day of the week, is the average number of visits at the locations and setting, measured over 5 consecutive weeks pre-pandemic, between Jan 3 and Feb 6, 2020. The daily number of visits in a setting is then divided by the baseline number in that setting of the corresponding weekday, and scaled so that 0 corresponds to the baseline level, 100 corresponds to a doubling in the number of visitors and, e.g., −50 corresponds to a reduction in visitors by 50%. The residential and workplace settings measure the length of stay (in minutes) during a 24 hour period rather than number of visits and are otherwise defined analogously. An unspecified, small amount of noise is added to the data before computation of the baseline values and the daily counts to meet anonymity requirements [20].

Let denote the Google covariate used in our model, at day t in region r in setting k. We have rescaled the data provided by Google, such that , corresponds to a 50% reduction in activity level, corresponds to the same activity level as at baseline and corresponds to a 100% increase in activity. Furthermore we used a (right-aligned) 7-day moving average of the data for our model to deal with the inherent weekday fluctuations in the GCMR data. Fig. 1 in S1 Appendix shows the mean GCMR and variation across regions for Norway and Sweden, for the different settings.

Temperature

Daily average temperature for Norway was acquired from the Norwegian Meteorological Institute Frost API, while the Swedish temperature data was acquired through the Open Data Meteorological Observations API provided by Swedish Meteorological and Hydrological Institute. For each region a weather station close to the most dense populated area was selected. The full list of stations selected is given in Table 1 in S1 Appendix.

Variants of concern data

The World Health Organization (WHO) declared the Alpha variant (pango lineage B.1.1.7) a Variant of Concern (VoC) on December 18, 2020. On May 11, 2021, WHO classified Delta (pango lineage B.1.617.2) as a VoC. Ideally we want to know the proportion of the true number of cases that are of the different variants. This is unknown because the true incidence in the population is unknown and not every case was sequenced. Instead, we approximate the true proportion by the proportion of the sequenced/screened cases, denoted and for the Alpha and Delta variants, respectively. The share of Alpha and Delta variants over time was only available on a national level in a weekly temporal resolution. The same time series were therefore used for all regions within a country. Fig. 20 in S1 Appendix shows the data. For Norway, the data was acquired manually from the weekly Covid-19 reports of the National Institute of Public Health [21] and the Swedish data was acquired from the web pages of Public Health Agency of Sweden [22].

Vaccination data

Vaccination data is given as daily number of new individuals who have received the second vaccine dose, by region and by age group, denoted for day t, region r and age group i. See Table 2 in S1 Appendix for age groups. Data for Norway was downloaded from the GitHub of The Norwegian Institute of Public Health [23] and data for Sweden was provided from the Public Health Agency of Sweden upon request. The vaccine data were not updated every day of the week. We therefore assume a linear increase in the cumulative number of vaccinated individuals at days with missing data. See Fig. 22 - Fig. 24 in S1 Appendix.

Model for disease spread

We model the spread of disease over time in a region by a discrete time deterministic meta-population model, an age-structured SIR model (see Fig. 25 in S1 Appendix). The population in region r at day t and age-group i is divided into susceptible individuals , infectious individuals , individuals recovered from infection and vaccinated individuals V_t,r. Transitions between the compartments are given by the following set of equations:

where N_r is the population size of region r. Infectious individuals at day t, , interact homogeneously with the susceptible individuals in each age group. The transmissibility parameter , is defined as the average number of infectious contacts an infected individual has at day t in a fully susceptible population. We model this parameter as a function of region specific covariates and associated parameters are estimated. In addition to the susceptible individuals infected by individuals from the infectious compartments, we assume that n_imp per 100 000 susceptible individuals in each age group are infected each day and moved to their respective infectious compartment, to mimic importation of cases. In our main analysis, we specified n_imp = 0.5. Infectious individuals in age group i are moved to the recovered naturally compartment with a rate of days.

The modeling period extends over a time period where vaccination was implemented. Age prioritized vaccination changes the age composition of the infected individuals, which then changes the risk of hospitalization. The likelihood of hospitalization at time t depends on the probability that a randomly selected susceptible individual belongs to a specific age group, hence, we need to keep track of the number of susceptible individuals in each age group. This motivates the age structure of the meta-population model.

Vaccinated individuals are assumed to either become fully immune, hence not contributing to further transmission of the disease, or else, with probability p_v the vaccine has no effect. The daily number of new individuals with full immunity from vaccine, , are removed from the susceptible and naturally recovered compartments, according to the relative size of and . Immunity is assumed to remain over the study period.

Parameterisation of transmissibility parameter

We want to relate the transmissibility parameter to multiple covariates: the GCMRs, temperature (as a proxy for seasonality) and share of specific virus variants. The different GMCR settings are assumed to have an additive effect on the transmissibility, while the temperature and the share of circulating virus variants are assumed to have a multiplicative effect.

The additive part of the transmissibility, , as a function of the GCMRs, is derived as follows. Assume that the average number of secondary infections of an infectious individual occur in K different settings, e.g., at work, public transport etc. For setting k, we define the average number of secondary infection at day t in region r, , as the product between the average number of contacts in that setting, , and the probability that a contact results in an infection, . The number of contacts in each setting is unknown. By assuming a linear association between the GCMRs and the number of contacts in a setting, the number of secondary infections in setting k becomes

where is the baseline level (pre-pandemic) number of contacts in setting k in region r. The parameter can be interpreted as the average daily secondary infections per infectious individual in region r, in setting k at the baseline activity level, i.e., pre-pandemic level when .

The number of secondary infections caused by an infectious individual during a day is then the sum of secondary infections in the different settings. In addition to the K settings, we include daily secondary infections happening outside of the considered GCMR transmission settings by adding a weekly region specific parameter, (e.g., household transmission), assumed to be a priori i.i.d. between weeks and across regions based on a half-normal prior with region-specific standard deviation (cf. Implementation). The additive part of the transmissibility at day t in region r is then

In our model fitting, we included K = 4 settings from the GCMR covariates: Grocery and pharmacy, Retail and recreation, Public transport and Workplace. We excluded the Park (not adding to transmission) and Home settings as the assumption of a linear increase in infectious contacts with increasing activity seems less plausible for these settings, and home setting having strong (negative correlation with the other factors.

Transmission dynamics are not only related to changes in contact frequencies. Seasonality and virus variants alter transmissiblity of a pathogen substantially. We use region-specific daily mean temperature as a proxy for seasonality and assume that the seasonality as well as the Alpha and Delta virus variants act multiplicatively on the transmissibility by changing the probability of infection upon contact. The multiplicative part of the transmissibility is modeled as

where is the temperature difference at day t compared to the first day of the analysis in region r, and and represent the fraction of individuals infected by the two variants of concern. The parameters , and are assumed constant over region and in time. The multiplicative change in transmission probability for a one-degree increase in temperature is then , and or correspond to a multiplicative increase in transmissibility for the Alpha or Delta VoC compared to the wild-type. To characterize the total effect of seasonality we focus on the multiplicative change for a difference in temperature of 20 degrees, , which corresponds to the median temperature difference between the average temperature in the warmest and coldest months of the year for the Norwegian and Swedish regions.

Combining the additive and multiplicative parts and , we get the final parameterization of the transmissibility

The parameters that we need to estimate in the above parameterization of are (for 75 week and each region), (for each region and K = 4 behaviour settings), , and .

Interpretation of model parameters and derived quantities

We focus on two aspects when interpreting the estimated parameters for the GCMRs. First, the proportion of variation in the additive part of transmissibility, which is explained by the linear model in combination with the observed change in the community mobility report data. For this purpose, we can quantify per region the mean share of mobility reports in over time: . We refer to this quantity as the mean share of daily infectious contacts in settings captured by the community mobility reports. A similar summary statistic also takes into account the time-varying number of susceptible and infected individuals: . It represents the overall share of secondary infections in settings captured by the community mobility reports model over the whole observation period. These calculations can be performed for all K = 4 categories of the GCMRs combined or for each category separately. A second aspect is related to which of the four considered community mobility reports captures population behavior that appears to be most relevant for disease transmission. This can be addressed by investigating the relative size of the coefficients for the K = 4 categories: . We perform posterior inference for these parameters per region and combine the region-specific estimates based on a population-weighted mean over all regions of a country.

Fitting the model

We fit the model to weekly number of new hospital admissions due to SARS-CoV-2 infection in each region. The number of hospital admission in week w is assumed to follow a Poisson distribution, with expectation dependent on daily new number of infected individuals, distribution of time between infection and hospitalization and risk of hospitalization given infection. Due to vaccination, the age distribution of the daily new infected individuals changes over time, which further changes the age-specific risk of hospitalization. For this reason, and the fact that hospitalization risk changes for different virus variants [24,25], the modeled risk of hospitalization is time dependent.

Hospital incidence data

Hospital incidence data for Norway was acquired by request from Norwegian Institute of Public Health. The data consist of weekly number of new hospital admission, for individuals with Covid-19 infection as main cause of hospitalization, for each of the 11 Norwegian regions.

Swedish data on hospital incidence was obtained from Socialstyrelsen [26]. They provide data on the weekly hospital incidence on a national level, as well as the number of currently treated individuals (occupied beds) on the county-level. County-level hospital incidence was not directly available. To approximate weekly hospital-incidence on the county-level, we distributed the national incidence to the counties based on the relative share of all individuals treated per county within the respective week.

Likelihood of hospitalizations

The number of new hospitalizations, H_w,r, in week w in region r was modeled by a Poisson distribution,

(1)

where denotes the probability of being hospitalized if infected at day t and belonging to region r; m is the maximum number of days from infection to hospitalization and denotes the probability of going to hospital j days after infection, given that an infected individual goes to hospital. The quantity u_t,r is the number of new infections at day t in region r in our model, given by the sum of infections and imported cases

If all infected individuals were hospitalized, then the expected number of individuals sent to hospital at day t will be the sum, over the preceding m days, of the number of new infections j days before day t, times the probability that those new infections are hospitalized after j days, i.e., at day t. Not all infected individuals need hospitalization, and we therefore multiply by , the probability that an individual infected at day t − j goes to hospital at day t (age-differences taken into account as explained below). The expected new hospitalizations in week w is then the sum over all days t in week w.

Distribution of time between infection and hospitalization

The probability of being hospitalized j days after infection, given that an infected individual gets hospitalized, is denoted . The time from infection to hospitalization consists of a pre-symptomatic period (time from infectiousness starts to symptom onset), followed by the period from symptom onset to hospital admission. Following the situational awareness and forecasting reports [2], Week 51, 29 December 2021, we assume that the pre-symptomatic period is exponentially distributed with mean 2 days, i.e., Exp(1/2). Norwegian data on time from symptom onset to hospitalization, provided by FHI on request, fits well with a negative binomial distribution, with mean and over-dispersion parameter changing with time. We assume these parameters are constant in time, and therefore resample data from the negative binomial for each time period, and estimate the mean (7.93) and over-dispersion parameter (6.21) of a negative binomial distribution from this data set. We assume that the length of the pre-symptomatic period and the symptomatic period are independent, and hence, is expressed as the convolution between the exponential distribution of the pre-symptomatic period and the negative binomial distribution of the time from symptom onset to hospitalization.

Probability of hospitalization given infection

The probability of being hospitalized if SARS-CoV-2 infected is highly age dependent. The age distribution of the infected individuals in a region changes with age prioritized vaccination. The probability of hospitalization is also affected by the circulating virus variants. In the above likelihood of hospitalizations, the region specific parameter is time dependent, but not age specific. We therefore need the time variation of the parameter to take into account both the changing age distribution of the infected individuals and the changing proportion of virus variants.

Let be the probability that an individual in region r infected at day t goes to hospital, given that the individual belongs to age group i. The probability that an individual infected at time t in region r is admitted to hospital is expressed as

where is the fraction of the susceptibles being in age group i in region r at day t. We have used values for for the “wild-type” variant as given in the FHI modeling reports [2]. These probabilities are built on work by Salje et al. [27] and adjusted to fit a Norwegian population. However, vaccine data both for Norway and Sweden have different age groups, so we need to transform these probabilities to fit other age groups. A simple approach to this is to fit the exponential function y = e^(a+bx), where x denotes age, to the Norwegian specific probabilities. The estimated coefficients were a = −2.52 and b = 0.06. Probabilities for the new age groups were then inferred by choosing the fitted value y that corresponds to the middle age of each age group. See Fig 21 and Table 2 in S1 Appendix for age specific hospitalization risk for Norway and Sweden.

These risks of going to hospital for a given virus variant and age group is assumed constant throughout the pandemic, however, they change for different virus variants. The proportion of the different variant among the infectious individuals change over time, and hence do the risk of hospitalization. The risk of going to hospital if infected with the Alpha variant is estimated to be 1.9 times higher than if infected by the Wild-type [24,25]. The same holds for the Delta variant. This increase in hospitalization risk is assumed to be the same for all age groups. The overall risk of going to hospital, given infection, in terms of the proportion of the Alpha variant and Delta variant is then

We only have access to variant data on a national level and therefore use the same data for all region within a country, despite the variants have probably spread differently in the different regions [21].

Implementation

The meta-population and data model was implemented in Stan using the cmdstanr R-package to facilitate parameter estimation via Hamiltonian Monte Carlo. For a model fit to n^reg regions (11 for Norway, 21 for Sweden, and 2 for Germany) with 4 GCMR categories, 3 multiplicative factors on transmissibility (Temperature, and change in tranmissibility for Alpha and Delta VoC) in a period of n^week weeks (75 for Norway/Sweden, 44 for Germany) we estimated

parameters and hyper-parameters. We used the Normal and (truncated) Half-normal priors as shown in Table 1:

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Table 1. Priors used for model fitting.

https://doi.org/10.1371/journal.pgph.0006368.t001

The data model for the region-specific weekly hospitalization counts consisted of a Poisson Likelihood as described above. The model was fitted using 4 independent chains with with 1000 samples (200 warm-up) each and convergence was monitored based on standard diagnostics ( for all parameters and visual investigation of trace plots). Source code including the Stan-model as well as the full analysis pipeline for the public data from Germany (based on the targets R-package) are provided in a Github repository https://github.com/FelixGuenther/nordic_behavior_public.

Analysis for German regions

For fitting our model to two German regions we used 44 weekly data points on the reported 7-day hospitalization incidence provided by the Robert Koch-Institute from 1 March, 2021 to 27 December, 2022 for the federal states of Berlin and Bavaria [28]. These measurements contain all reported hospital cases from the last 7 days. We collected the publicly available GCMRs and obtained temperature data from the publicly available database of Deutscher Wetterdienst. As this analysis was focused on the year 2021 only, no data on vaccination or VoCs was required. Otherwise, model specification and fitting was performed as in the analysis for Norwegian and Swedish counties with one exception: as the population size of the German federal states is substantially larger compared to the Nordic counties (3.7 and 13.1 Million for Berlin/Bavaria) we reduced the daily importation of infectious individuals from 0.5/100,000 to 0.1/100,000 individuals to avoid an unrealistically high assumption on (absolute) imported cases, in particular during low-incidence periods.