Behavioral changes before lockdown and decreased retail and recreation mobility during lockdown contributed most to controlling COVID-19 in Western countries

Background The COVID-19 pandemic has prompted a lockdown in many countries to control the exponential spread of the SARS-CoV-2 virus, hereby reducing the time-varying basic reproduction number (Rt) to below one. Governments are looking for evidence to balance the demand of their citizens to ease some of the restriction, against the fear of a new peak in infections. In this study, we wanted to quantify the relative contribution of mobility restrictions, and that of behavioral changes that occurred already before the lockdowns, on the reduction of transmission during lockdowns in Western countries in early 2020. Methods Incidence data of cases and deaths from the first wave of infections for 35 Western countries (32 European, plus Israel, USA and Canada) were analyzed using epidemiological compartment models in a Bayesian framework. Mobility data was used to estimate the timing of changes associated with a lockdown, and was correlated with estimated reductions of Rt. Results Across all countries, the initial median estimate for Rt was 3.6 (95% IQR 2.4–5.2), and it was reduced to 0.78 (95% IQR 0.58–1.01) during lockdown. 48% (18–65%) of the reduction occurred already in the week before lockdown, with lockdown itself causing the remaining drop in transmission. A lower Rt during lockdown was independently associated with an increased time spent at home (0.21 per 10% more time, p < 0.007), and decreased mobility related to retail and recreation (0.07 per 10% less mobility, p < 0.008). Conclusions In a Western population unaware of the risk, SARS-CoV-2 can be highly contagious with a reproduction number R0 > 5. Our results are consistent with evidence that recreational activities (including restaurant and bar visits) enable super-spreading events. Exiting from lockdown therefore requires continued physical distancing and tight control on this kind of activities. Supplementary Information The online version contains supplementary material available at 10.1186/s12889-021-10676-1.

The data collected on cases and deaths are related to infections through biological and clinical processes, but also impacted by other unknown delays, such as testing and reporting practices. The time from infection to confirmed test depends largely on whether the diagnosis was performed based on presence of mild symptoms (which were in many countries not officially tested during the initial phase of the outbreak because of shortages of test kits), or whether the test was performed at the time of hospitalization, or whether the tests was done early on within the context of contact tracing. Time between infection and reported death may be dependent on treatment availability, clinical choices and practices, but also on reporting delays due to disparate policies in different countries.
Here we assumed for both periods a gamma distribution, and co-estimated the shape k and scale θ parameters. Incidence of diagnosed cases C(t) and deaths D(t) were then derived from the state of the SEIR model by convolving a Gamma density function function Γ(k c , θ c ) and Γ(k d , θ d ) over the number of new infections (transitioning from S to E compartment), with a rate of ρ c (test rate) and ρ d (infection fatality rate).
The parameters k and θ were co-estimated using a parameterization of their mean µ and standard deviation σ. Because the dates of mobility changes d 1 and d 2 were independently estimated from Google Mobility data, the incidence data was informative for the identification of these distribution parameters, and given the uncertainty as discussed above, a uniform prior was chosen for their mean µ. Initial experiments with an informative prior σ = 8.5 used by Flexman et al. (1) resulted in bad model fits for a number of countries (including Netherlands, Spain, and Switzerland), due to the inability of the model to capture the fast rise and fall of cases and deaths (see for example for Spain in Figure 1). This can be explained by considering that the infection-to-case and infection-to-death distributions may be interpreted as stepped impedence resonator (SIR) low pass filters of new infections over time, thus limiting the rate at which changes in the resulting time curves of incidence of confirmed tests and deaths may occur: a Gamma distribution with σ = 8.5 days was calculated to have a 20 dB stop-band cut-off at 1/20 day−1 using freqz, which intuitively implies that changes cannot occur faster than in 20 days. When using less informative priors, lower values for σ 5 were being estimated instead. The estimate of µ d = 8.5 by Flexman et al. (1) was based on the combination of estimated infection-to-onset distributions (incubation period) and onset-to-death distributions from clinical date of the Wuhan epidemic, assuming independence. Our analysis thus suggests that incubation time and onset-to-death are not independent, and a longer incubation time is associated with a shorter period for onset-to-death.

Data fitting of cases and deaths
For the likelihood calculation for each incidence data point (number of cases or number of deaths) a negative binomial distribution was used with µ equal to the expected count, and a suitable dispersion parameter r. Death incidence data was considered more trustworthy than case reporting (which is influenced also by a possibly changing testing strategy). Therefore, a low value r c = 3 was used to reflect a low weight given to case date, while a higher value for the dispersion parameter r d = 60 was used since the data for incidence of deaths is expected to be more reliable, but accounting for observed variance due to clustering effects and outliers (presumably caused by back-reported deaths) seen in several countries.

Assumed constants and prior distributions
The average generation time G was assumed a constant and calculated as T lat + 1/(2T inf ) (2). Table 1 lists the model parameters and their initial values or prior distributions for three models used in the analyses.
initial Exposed count 1 initial Infectious count 0

Statistical analyses
For multivariate models, collinearity was assessed by calculating variance-inflation factors using vif. Variance-inflation factors higher than 6 were considered problematic, they were removed starting iteratively with the highest value. The average effect of a mobility change on reduction of R t,2 was estimated by applying the estimated effect to the median mobility reduction in the 35 analyzed countries. For example, for retail and recreation on the estimated effect (-0.07 +/-0.02 per 10% mobility reduction) was applied to the median mobility reduction of -66%. Similarly, the upper bound of the impact of increased mobility to parks was estimated by applying the estimated effect (-0.021 +/-0.009 per 10% mobility increase) to the 95% upper quantile of the mobility in the 35 analyzed countries (+53%).
To evaluate whether the R t,2 value in Sweden could equally be explained by the linear model using changes in mobility, the influence of the data for Sweden was diagnosed using lm.influence (leave-one-out cross-validation) and the residual error of the model prediction was compared to the residual error distribution.

Model parameter estimates
The time curves for each country estimated using model-2 are shown in Suppl 4 and parameter estimates are summarized in Tables 2 and 3.

Model with an additional transition point for R t during lockdown
Since the initial model model-2 was found to not be applicable to the data of Slovakia, a model model-3p with an additional transition point for R t during lockdown was considered. To allow this transition point to be identified, all data (until June 3th) was used to fit this model. To obtain realistic models even for countries with a low amount of cases (such as Slovakia), informative priors were used based on estimates from model-2. Support for the additional transition point was evaluated using Deviance Information Criterion (DIC (6)) in comparison with a model model-2p that was estimated on the same data with the same priors but without the additional change point. DIC was from the posterior MCMC samples using: The resulting estimates for the additional change of transmission during lockdown is indicated in Table 4. For 11 of the 35 countries (Bosnia and Herzegovina, Canada, Croatia, Germany, Italy, Netherlands, Romania, Serbia, Slovakia, Slovenia, and Switzerland), a reduction of transmission was found during lockdown (where ∆DIC < −5), for 3 countries (North Macedonia, Portugal and Spain) a signicant increase of transmission, and for the remaining 21 countries no significant change in transmission during lockdown was detected. The reason for these detected changes may be a real change in transmission, but could also be due to some of the limitations inherent to the model or data (see limitations discussed in the main article). That for a large majority of the countries no significant change in transmission was observed during lockdown does however confirm that lockdown was indeed the final effective measure for controlling transmission in these countries.

Robustness to different assumptions of the duration of the latent period
To assess the robustness of the findings to different assumptions of latent period duration T lat (which was assumed to be 3 days), models were re-estimated using an assumption of 2 and 4 days, by keeping generation time the same (and thus by varying T inf as well). Table 5 shows the parameter estimates for each of the three assumptions of duration of the latent period. Since the duration of the infectious period decreased as latent period increased, the main observation is a reduction of R t values larger than 1, and an increase of R t values smaller than 1.
Univariate associations between different independent predictors (mobility changes in different categories and test rate) showed the same trend and had the same statistical significance using different assumed periods for T lat (Tables 6  and 7). The improved fit when assuming a lower latent period duration of 2 days would suggest that this value of 2 is more suitable, implying that on average about 3 days of presymptomatic transmission occurs.

Robustness to different assumptions of the duration of generation time
To assess the robustness of the findings to different assumptions of generation time G (which was assumed to be 5.2 days), models were re-estimated using an assumption of 4.5 and 5.9 days, by keeping latent period duration the same (and thus by changing T inf ). Table 8 shows the parameter estimates for each of the three assumptions of duration of the latent period. Since the duration of the infectious period increased as generation time increased, the main observation is an increase of R t values larger than 1, and an decrease of R t values smaller than 1.
Univariate associations between different independent predictors (mobility changes in different categories and test rate) showed the same trend and had the same statistical significance using different assumed periods for T lat (Tables 9 and 10).