Google Mobility utilisesdata from the Google Maps system and other platforms, it measures the amount of mobility in the categories in six categories presented in Table 1. The numbers are reported as the percentage change from a baseline level.
Table 1. Public mobility data categories.
Retail and Recreation
restaurants, cafes, shopping centers, theme parks, museums, libraries, and movie theaters
Grocery and Pharmacy
grocery markets, food warehouses, farmers markets, specialty food shops, drug stores, and pharmacies
subway, bus, and train stations
local parks, national parks, public beaches, marinas, dog parks, plazas, and public gardens
places of work
The government-level of restrictions is quantified in a project known as the Oxford COVID-19 Government Response operated by the Blavatnik School of Government at the University of Oxford. It incorporates a wide variety of different restrictions related to social distancing in the wake of the pandemic and serves as a benchmark on how much each administration enforced lockdown. The Stringency Index is a weighted average of several categories , including school closures, workplace closures, cancellation of public events, restrictions on public gatherings, closures of public transport, stay-at-home requirements, public information campaigns, restrictions on internal movements, and international travel controls.
Temperature data were collected from the German Weather Service (DWD). The daily average at the Berlin-Tegel station was used as an aggregate for each day in the studied period.
R-values were obtained from the Robert Koch Institute derived from a now-casting model which has been used to forecast virus propagation on national and local levels . Through time series analysis of the number of new cases per day, an instantaneous reproduction number can be derived retrospectively for each day .
The period of March 9, 2020 through June 22, 2021 was studied.
Spearman correlations were used to identify associations between:
a) Oxford Stringency Index and the various mobilities
b) Mobilities and reproduction values
Gaussian Process Regression
An exponential–logarithmic model has been identified as an adequate fit for the association between community mobilities and reproduction rates [23-24], i.e. the logarithm of the R-value is dependent on aggregate mobility. It has also been identified that both temperature and level of vaccinations have an impact on reproduction [25-26].
Gaussian Process Regression (GPR) is a nonparametric supervised machine learning method usually applied to multivariate classification and regression problems . GPR is used for describing the original distribution for flexible classification and regression models, where regression or class probability functions are not only simple parametric forms. One of the main advantages of the Gaussian process is the diversity of covariance functions that leads to the formation of functions with distinct types or degrees of continuous structures and enables choosing the proper selection.
Based on these previous findings it was possible to fit a GPR model for the relationship between mobility, temperature, and vaccinations with the following setup:
Kernel function: Exponential , Kernel scale: 14.396 , Signal standard deviation: 0.230 ,
Training data: 80 % of observations, randomly chosen, Test data: Remaining 20 %