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Comparing COVID-19 response strategies across nations is a key step in preparing for future pandemics. Conventional comparisons, which rank individual non-pharmaceutical intervention (NPI) effects, are limited by: (i) a focus on epidemiological outcomes; (ii) NPIs typically being applied as packages of interventions; and (iii) different political, economic and social conditions among nations. Here, we develop a coupled epidemiological–behavioural–macroeconomic model that can transfer NPI effects from a reference nation to a focal nation. This approach quantifies epidemiological, behavioural and economic outcomes while accounting for both packaged NPIs and differing conditions among nations. As a first proof of concept, we take Germany as our focal nation during Spring 2020, and New Zealand and Switzerland as reference nations with contrasting NPI strategies. Our results suggest that, while New Zealand’s more aggressive strategy would have yielded modest epidemiological gains in Germany, it would have resulted in substantially higher economic costs while dramatically reducing social contacts. In contrast, Switzerland’s more lenient strategy would have prolonged the first wave in Germany, but would also have increased relative costs. More generally, these findings indicate that our approach can provide novel, multifaceted insights on the efficacy of pandemic response strategies, and therefore merits further exploration and development.

Despite the increasing use of standards for documenting and testing agent-based models (ABMs) and sharing of open access code, most ABMs are still developed from scratch. This is not only inefficient, but also leads to ad hoc and often inconsistent implementations of the same theories in computational code and delays progress in the exploration of the functioning of complex social-ecological systems (SES). We argue that reusable building blocks (RBBs) known from professional software development can mitigate these issues. An RBB is a submodel that represents a particular mechanism or process that is relevant across many ABMs in an application domain, such as plant competition in vegetation models, or reinforcement learning in a behavioural model. RBBs need to be distinguished from modules, which represent entire subsystems and include more than one mechanism and process. While linking modules faces the same challenges as integrating different models in general, RBBs are “atomic” enough to be more easily re-used in different contexts. We describe and provide examples from different domains for how and why building blocks are used in software development, and the benefits of doing so for the ABM community and to individual modellers. We propose a template to guide the development and publication of RBBs and provide example RBBs that use this template. Most importantly, we propose and initiate a strategy for community-based development, sharing and use of RBBs. Individual modellers can have a much greater impact in their field with an RBB than with a single paper, while the community will benefit from increased coherence, facilitating the development of theory for both the behaviour of agents and the systems they form. We invite peers to upload and share their RBBs via our website - preferably referenced by a DOI (digital object identifier obtained e.g. via Zenodo). After a critical mass of candidate RBBs has accumulated, feedback and discussion can take place and both

Changes in human behaviors, such as reductions of physical contacts and the adoption of preventive measures, impact the transmission of infectious diseases considerably. Behavioral adaptations may be the result of individuals aiming to protect themselves or mere responses to public containment measures, or a combination of both. What drives autonomous and policy-induced adaptation, how they are related and change over time is insufficiently understood. Here, we develop a framework for more precise analysis of behavioral adaptation, focusing on confluence, interactions and time variance of autonomous and policy-induced adaptation. We carry out an empirical analysis of Germany during the fall of 2020 and beyond. Subsequently, we discuss how behavioral adaptation processes can be better represented in behavioral-epidemiological models. We find that our framework is useful to understand the interplay of autonomous and policy-induced adaptation as a “moving target”. Our empirical analysis suggests that mobility patterns in Germany changed significantly due to both autonomous and policy-induced adaption, with potentially weaker effects over time due to decreasing risk signals, diminishing risk perceptions and an erosion of trust in the government. We find that while a number of simulation and prediction models have made great efforts to represent behavioral adaptation, the interplay of autonomous and policy-induced adaption needs to be better understood to construct convincing counterfactual scenarios for policy analysis. The insights presented here are of interest to modelers and policy makers aiming to understand and account for behaviors during a pandemic response more accurately.

Despite the increasing use of standards for documenting and testing agent-based models (ABMs) and sharing of open access code, most ABMs are still developed from scratch. This is not only inefficient, but also leads to ad hoc and often inconsistent implementations of the same theories in computational code and delays progress in the exploration of the functioning of complex social-ecological systems (SES). We argue that reusable building blocks (RBBs) known from professional software development can mitigate these issues. An RBB is a submodel that represents a particular mechanism or process that is relevant across many ABMs in an application domain, such as plant competition in vegetation models, or reinforcement learning in a behavioural model. RBBs need to be distinguished from modules, which represent entire subsystems and include more than one mechanism and process. While linking modules faces the same challenges as integrating different models in general, RBBs are “atomic” enough to be more easily re-used in different contexts. We describe and provide examples from different domains for how and why building blocks are used in software development, and the benefits of doing so for the ABM community and to individual modellers. We propose a template to guide the development and publication of RBBs and provide example RBBs that use this template. Most importantly, we propose and initiate a strategy for community-based development, sharing and use of RBBs. Individual modellers can have a much greater impact in their field with an RBB than with a single paper, while the community will benefit from increased coherence, facilitating the development of theory for both the behaviour of agents and the systems they form. We invite peers to upload and share their RBBs via our website - preferably referenced by a DOI (digital object identifier obtained e.g. via Zenodo). After a critical mass of candidate RBBs has accumulated, feedback and discussion can take place and b, Energie and Industrie, Policy Analysis

Comparing COVID-19 non-pharmaceutical intervention (NPI) strategies across nations is a key step in preparing for future pandemics. Conventional comparisons, which rank individual NPI effects, are limited by: 1) vastly different political, economic, and social conditions among nations, 2) NPIs typically being applied as packages of interventions, and 3) an exclusive focus on epidemiological outcomes of interventions. Here, we develop a coupled epidemiological-behavioural-macroeconomic model that allows us to transfer NPI strategies from a reference nation to a focal nation while preserving the packaged nature of NPIs, controlling for differences among nations, and quantifying epidemiological, behavioural and economic outcomes. As a demonstration, we take Germany as our focal nation during Spring 2020, and New Zealand and Switzerland as reference nations with contrasting NPI strategies. We show that, while New Zealand's more aggressive strategy would have yielded modest epidemiological gains in Germany, it would have resulted in substantially higher economic costs while dramatically reducing social contacts. In contrast, Switzerland's more lenient NPI strategy would have prolonged the first wave in Germany, but would have also have increased relative costs. Our results demonstrate that Germany's intermediate strategy was effective in quelling the first wave while mitigating both economic and social costs.

Geostatistics as a subfield of statistics accounts for the spatial correlations encountered in many applications of, for example, earth sciences. Valuable information can be extracted from these correlations, also helping to address the often encountered burden of data scarcity. Despite the value of additional data, the use of geostatistics still falls short of its potential. This problem is often connected to the lack of user-friendly software hampering the use and application of geostatistics. We therefore present GSTools, a Python-based software suite for solving a wide range of geostatistical problems. We chose Python due to its unique balance between usability, flexibility, and efficiency and due to its adoption in the scientific community. GSTools provides methods for generating random fields; it can perform kriging, variogram estimation and much more. We demonstrate its abilities by virtue of a series of example applications detailing their use.

The global extent and temporally asynchronous pattern of COVID-19 spread have repeatedly highlighted the role of international borders in the fight against the pandemic. Additionally, the deluge of high resolution, spatially referenced epidemiological data generated by the pandemic provides new opportunities to study disease transmission at heretofore inaccessible scales. Existing studies of cross-border infection fluxes, for both COVID-19 and other diseases, have largely focused on characterizing overall border effects. Here, we couple fine-scale incidence data with localized regression models to quantify spatial variation in the inhibitory effect of an international border. We take as a case study the border region between the German state of Saxony and the neighboring regions in northwestern Czechia, where municipality-level COVID-19 incidence data are available on both sides of the border. Consistent with past studies, we find an overall inhibitory effect of the border, but with a clear asymmetry, where the inhibitory effect is stronger from Saxony to Czechia than vice versa. Furthermore, we identify marked spatial variation along the border in the degree to which disease spread was inhibited. In particular, the area around Löbau in Saxony appears to have been a hotspot for cross-border disease transmission. The ability to identify infection flux hotspots along international borders may help to tailor monitoring programs and response measures to more effectively limit disease spread.

Throughout the coronavirus disease 2019 (COVID-19) pandemic, decision makers have relied on forecasting models to determine and implement non-pharmaceutical interventions (NPI). In building the forecasting models, continuously updated datasets from various stakeholders including developers, analysts, and testers are required to provide precise predictions. Here we report the design of a scalable pipeline which serves as a data synchronization to support inter-country top-down spatiotemporal observations and forecasting models of COVID-19, named the where2test, for Germany, Czechia and Poland. We have built an operational data store (ODS) using PostgreSQL to continuously consolidate datasets from multiple data sources, perform collaborative work, facilitate high performance data analysis, and trace changes. The ODS has been built not only to store the COVID-19 data from Germany, Czechia, and Poland but also other areas. Employing the dimensional fact model, a schema of metadata is capable of synchronizing the various structures of data from those regions, and is scalable to the entire world. Next, the ODS is populated using batch Extract, Transfer, and Load (ETL) jobs. The SQL queries are subsequently created to reduce the need for pre-processing data for users. The data can then support not only forecasting using a version-controlled Arima-Holt model and other analyses to support decision making, but also risk calculator and optimisation apps [1, 2]. The data synchronization runs at a daily interval, which is displayed at https://www.where2test.de.

Geostatistics as a subfield of statistics accounts for the spatial correlations encountered in many applications of, for example, earth sciences. Valuable information can be extracted from these correlations, also helping to address the often encountered burden of data scarcity. Despite the value of additional data, the use of geostatistics still falls short of its potential. This problem is often connected to the lack of user-friendly software hampering the use and application of geostatistics. We therefore present GSTools, a Python-based software suite for solving a wide range of geostatistical problems. We chose Python due to its unique balance between usability, flexibility, and efficiency and due to its adoption in the scientific community. GSTools provides methods for generating random fields; it can perform kriging, variogram estimation and much more. We demonstrate its abilities by virtue of a series of example applications detailing their use.

The SARS-CoV-2 virus has spread around the world with over 100 million infections to date, and currently many countries are fighting the second wave of infections. With neither sufficient vaccination capacity nor effective medication, non-pharmaceutical interventions (NPIs) remain the measure of choice. However, NPIs place a great burden on society, the mental health of individuals, and economics. Therefore the cost/benefit ratio must be carefully balanced and a target-oriented small-scale implementation of these NPIs could help achieve this balance. To this end, we introduce a modified SEIRD-class compartment model and parametrize it locally for all 412 districts of Germany. The NPIs are modeled at district level by time varying contact rates. This high spatial resolution makes it possible to apply geostatistical methods to analyse the spatial patterns of the pandemic in Germany and to compare the results of different spatial resolutions. We find that the modified SEIRD model can successfully be fitted to the COVID-19 cases in German districts, states, and also nationwide. We propose the correlation length as a further measure, besides the weekly incidence rates, to describe the current situation of the epidemic.

The improvement of process representations in hydrological models is often only driven by the modelers’ knowledge and data availability. We present a comprehensive comparison between two hydrological models of different complexity that is developed to support 1) the understanding of the differences between model structures and 2) the identification of the observations needed for model assessment and improvement. The comparison is conducted on both space and time and by aggregating the outputs at different spatio‐temporal scales. In the present study, mHM, a process‐based hydrological model and ParFlow‐CLM, an integrated subsurface‐surface hydrological model, are used. The models are applied in a mesoscale catchment in Germany. Both models agree in the simulated river discharge at the outlet and the surface soil moisture dynamics, lending their supports for some model applications (drought monitoring). Different model sensitivities are, however, found when comparing evapotranspiration and soil moisture at different soil depths. The analysis supports the need of observations within the catchment for model assessment, but it indicates that different strategies should be considered for the different variables. Evapotranspiration measurements are needed at daily resolution across several locations while highly‐resolved spatially distributed observations with lower temporal frequency are required for soil moisture. Finally, the results show the impact of the shallow groundwater system simulated by ParFlow‐CLM and the need to account for the related soil moisture re‐distribution. Our comparison strategy can be applied to other models types and environmental conditions to strengthen the dialog between modelers and experimentalists for improving process representations in Earth system models.

Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the concentration variance, used in moment methods. The mixing model, describing the transport of the PDF in concentration space, is essential for both methods. Finding a satisfactory mixing model is still an open question and due to the rather elaborate PDF methods, a difficult undertaking. Both the PDF equation and the concentration variance equation depend on the same mixing model. This connection is used to find and test an improved mixing model for the much easier to handle concentration variance. Subsequently, this mixing model is transferred to the PDF equation and tested. The newly proposed mixing model yields significantly improved results for both variance modelling and PDF modelling.

Evolution equations for probability density functions (PDFs) and filtered density functions (FDFs) of random species concentrations weighted by conserved scalars are formulated as Fokker–Planck equations describing stochastically equivalent processes in concentration-position spaces. This approach provides consistent numerical PDF/FDF solutions, given by the density in the concentration-position space of an ensemble of computational particles governed by the associated Itô equations. The solutions are obtained by a global random walk (GRW) algorithm, which is stable, free of numerical diffusion, and practically insensitive to the increase of the number of particles. The general FDF approach and the GRW numerical solution are illustrated for a reduced complexity problem consisting of the transport of a single scalar in groundwater. Randomness is induced by the stochastic parameterization of the hydraulic conductivity, characterized by short range correlations and small variance. The objective is to infer the statistics of the random concentration sampled at the plume center of mass, integrated over the transverse dimension of a two-dimensional spatial domain. The PDF/FDF problem can therefore be formulated in a two-dimensional domain as well, a spatial dimension and one in the concentration space. The upscaled drift and diffusion coefficients describing the PDF transport in the physical space are estimated on single-trajectories of diffusion in velocity fields with short-range correlations, owing to their self-averaging property. The mixing coefficients describing the PDF transport in concentration spaces are parameterized by the trend and the noise inferred from the statistical analysis of an ensemble of simulated concentration time series, as well as by classical mixing models. A Gaussian spatial filter applied to a Kraichnan velocity field generator is used to construct coarse-grained simulations (CGS) for FDF problems. The purposes of the CGS simulations are two

Concentrations of chemical species transported in random environments need to be statistically characterized by probability density functions (PDF). Solutions to evolution equations for the one-point one-time PDF are usually based on systems of computational particles described by Ito equations. We establish consistency conditions relating the concentration statistics to that of the Ito process and the solution of its associated Fokker-Planck equation to that of the PDF equation. In this frame, we use a recently proposed numerical method which approximates PDFs by particle densities obtained with a global random walk (GRW) algorithm. The GRW-PDF approach is illustrated for a problem of contaminant transport in groundwater.

We identify sufficient conditions under which evolution equations for probability density functions (PDF) of random concentrations are equivalent to Fokker–Planck equations. The novelty of our approach is that it allows consistent PDF approximations by densities of computational particles governed by Itô processes in concentration–position spaces. Accurate numerical solutions are obtained with a global random walk (GRW) algorithm, stable, free of numerical diffusion, and insensitive to the increase of the total number of computational particles. The system of Itô equations is specified by drift and diffusion coefficients describing the PDF transport in the physical space, provided by up-scaling procedures, as well as by drift and mixing coefficients describing the PDF transport in concentration spaces. Mixing models can be obtained similarly to classical PDF approaches or, alternatively, from measured or simulated concentration time series. We compare their performance for a GRW-PDF numerical solution to a problem of contaminant transport in heterogeneous groundwater systems.