Monitoring Public Behavior During a Pandemic Using Surveys: Proof-of-Concept Via Epidemic Modelling

Implementing a lockdown for disease mitigation is a balancing act: Non-pharmaceutical interventions can reduce disease transmission significantly, but interventions also have considerable societal costs. Therefore, decision-makers need near real-time information to calibrate the level of restrictions. We fielded daily surveys in Denmark during the second wave of the COVID-19 pandemic to monitor public response to the announced lockdown. A key question asked respondents to state their number of close contacts within the past 24 hours. Here, we establish a link between survey data, mobility data, and, hospitalizations via epidemic modeling. Using Bayesian analysis, we then evaluate the usefulness of survey responses as a tool to monitor the effects of lockdown and then compare the predictive performance to that of mobility data. We find that, unlike mobility, self-reported contacts track the immediate behavioral response after the lockdown's announcement, weeks before the lockdown's national implementation. The survey data agree with the inferred effective reproduction number and their addition to the model results in greater improvement of predictive performance than mobility data. A detailed analysis of contact types indicates that disease transmission is driven by friends and strangers, whereas contacts to colleagues and family members (outside the household) only played a minor role despite Christmas holidays. Our work shows that an announcement of non-pharmaceutical interventions can lead to immediate behavioral responses, weeks before the actual implementation. Specifically, we find that self-reported contacts capture this early signal and thus qualify as a reliable, non-privacy invasive monitoring tool to track the implementation of non-pharmaceutical interventions

Linking social network structure and function to social preferences

Social network structures play an important role in the lives of humans and non-human animals by affecting wellbeing, the spread of disease and information, and evolutionary processes. Nevertheless, we still lack a good understanding of how these structures emerge from individual behaviour. Here we present a general model for the emergence of social structures, which is based on a key aspect of real social systems observed across species, namely social preferences for traits (individual characteristics such as age, sex, etc.). We first show that the model can generate diverse artificial social structures, and consider its potential for being combined with real network data. We then use the model to gain fundamental insights into how two main categories of social preferences (similarity and popularity) affect social structure and function. The results show that the types of social preference, in combination with the types of trait they are used with, can have important consequences for the spread of information and disease, and the robustness of social structures against fragmentation. The results also suggest that symmetric degree distributions could be expected to be common in social networks. More generally, the study implies that trait-based social preferences can have consequences for social systems that go far beyond their effect on direct benefits from social partners. We discuss the implications of the results for social evolution.Comment: 19 pages, + 16 pages supplementary material. 4 figures, + 11 supplementary figure

Disease spread through animal movements: a static and temporal network analysis of pig trade in Germany

Background: Animal trade plays an important role for the spread of infectious diseases in livestock populations. As a case study, we consider pig trade in Germany, where trade actors (agricultural premises) form a complex network. The central question is how infectious diseases can potentially spread within the system of trade contacts. We address this question by analyzing the underlying network of animal movements. Methodology/Findings: The considered pig trade dataset spans several years and is analyzed with respect to its potential to spread infectious diseases. Focusing on measurements of network-topological properties, we avoid the usage of external parameters, since these properties are independent of specific pathogens. They are on the contrary of great importance for understanding any general spreading process on this particular network. We analyze the system using different network models, which include varying amounts of information: (i) static network, (ii) network as a time series of uncorrelated snapshots, (iii) temporal network, where causality is explicitly taken into account. Findings: Our approach provides a general framework for a topological-temporal characterization of livestock trade networks. We find that a static network view captures many relevant aspects of the trade system, and premises can be classified into two clearly defined risk classes. Moreover, our results allow for an efficient allocation strategy for intervention measures using centrality measures. Data on trade volume does barely alter the results and is therefore of secondary importance. Although a static network description yields useful results, the temporal resolution of data plays an outstanding role for an in-depth understanding of spreading processes. This applies in particular for an accurate calculation of the maximum outbreak size.Comment: main text 33 pages, 17 figures, supporting information 7 pages, 7 figure

Early warning of infectious disease outbreaks on cattle-transport networks.

Surveillance of infectious diseases in livestock is traditionally carried out at the farms, which are the typical units of epidemiological investigations and interventions. In Central and Western Europe, high-quality, long-term time series of animal transports have become available and this opens the possibility to new approaches like sentinel surveillance. By comparing a sentinel surveillance scheme based on markets to one based on farms, the primary aim of this paper is to identify the smallest set of sentinel holdings that would reliably and timely detect emergent disease outbreaks in Swiss cattle. Using a data-driven approach, we simulate the spread of infectious diseases according to the reported or available daily cattle transport data in Switzerland over a four year period. Investigating the efficiency of surveillance at either market or farm level, we find that the most efficient early warning surveillance system [the smallest set of sentinels that timely and reliably detect outbreaks (small outbreaks at detection, short detection delays)] would be based on the former, rather than the latter. We show that a detection probability of 86% can be achieved by monitoring all 137 markets in the network. Additional 250 farm sentinels-selected according to their risk-need to be placed under surveillance so that the probability of first hitting one of these farm sentinels is at least as high as the probability of first hitting a market. Combining all markets and 1000 farms with highest risk of infection, these two levels together will lead to a detection probability of 99%. We conclude that the design of animal surveillance systems greatly benefits from the use of the existing abundant and detailed animal transport data especially in the case of highly dynamic cattle transport networks. Sentinel surveillance approaches can be tailored to complement existing farm risk-based and syndromic surveillance approaches

Krankheitsausbreitung auf Netzwerken mit statischen und zeitlich veränderlichen Topologien

We aim to develop epidemiological models that describe and predict the evolution of infectious diseases. To this end, we integrate mobility data, represented by networks with static and time-varying topologies. As a central result of this work, we present three disease models that facilitate an efficient analysis of complex epidemiological problems. First, in the context of global epidemics, we present a network-based measure, termed random-walk effective distance (RWED), as a proxy for the expected infection arrival time. Here, we use the global mobility network where nodes and edges represent urban regions and air traffic connections, respectively. The RWED integrates all potential transmission paths from the outbreak location to the target node and thus improves predictions about the course of a pandemic. Next, we are developing a matrix-based algorithm that integrates time-varying topologies with generic disease models. Based on Boolean algebra, we derive a reachability matrix in order to assess the vulnerability and damage potential of individual nodes in a temporal network. Finally, we present the so-called contact-based model as a versatile approach in which temporal edges instead of nodes form central elements of a dynamic system. This change of perspective improves previous, individual-based approaches for infectious diseases with permanent immunity. In particular, we derive an analytical criterium to determine the critical disease parameters that separate local and global outbreaks. The presented models integrate elements of statistical physics, nonlinear dynamics, and linear algebra to provide quantitative insights into epidemiological problems. We compare these analytical predictions with numerical models on numerous empirical mobility networks in order to evaluate the quality and limitations of our analytical approaches.Ziel dieser Arbeit ist es, epidemiologische Modelle zur Beschreibung infektiöser Krankheiten zu entwickeln. Dabei integrieren wir Mobilitätsdaten, die mathematisch durch Netzwerke mit statischen oder zeitlich veränderlichen Topologien beschrieben werden können. Als zentrales Ergebniss dieser Arbeit präsentieren wir drei Krankheitsmodelle, die eine effiziente Analyse komplexer Probleme gestatten. Zuerst stellen wir im Kontext globaler Epidemien ein Netzwerk-basiertes Maß vor und zwar die random-walk effective distance (RWED), mit dem die erwartete Ankunftszeit einer Krankheit abgeschätzt werden kann. Dazu gehen wir vom globalen Mobilitätsnetzwerk aus, in dem Knoten und Kanten urbane Regionen abstrahieren, die durch den globalen Flugverkehr verbunden sind. Die RWED berücksichtigt, entgegen früherer Methoden, alle potentiellen Übertragungswege vom Ausbruchsort bis zum Zielknoten und ermöglicht somit präzisere Vorhersagen zum Verlauf einer Pandemie. Als nächstes entwickeln wir einen Matrix-basierten Algorithmus, der zeitlich veränderliche Topologien mit generischen Krankheitsmodellen integriert. Durch boolesche Verknüpfungen leiten wir eine Erreichbarkeitsmatrix ab, mit der die Vulnerabilität und das Schadenspotential einzelner Knoten effizient untersucht werden können. Schließlich stellen wir mit dem Kontakt-basierten Modell einen versatilen Ansatz vor, in dem temporär auftretende Kanten statt Knoten zentrale Elemente eines dynamischen Systems sind. Dieser Perspektivwechsel ermöglicht präzisere Vorhersagen bei Infektionskrankheiten mit dauerhafter Immunität. Insbesonders leiten wir ein analytisches Kriterium ab, mit dem das Risiko eines globalen Krankheitsausbruchs effizient abgeschätzt werden kann. Die vorgestellten Modelle integrieren Elemente der statistischen Physik, nicht-linearen Dynamik und der linearen Algebra, um spezifische Fragestellungen der Epidemiologie zu beleuchten. Analytische Vorhersagen vergleichen wir mit numerischen Modellen auf zahlreichen empirischen Mobilitätsnetzwerken, um die Qualität und Grenzen unserer Methoden zu evaluieren.DFG, SFB 910, Kontrolle von zeitabhängigen Netzwerken und Anwendungen auf Epidemiologi

Epidemic modelling of monitoring public behavior using surveys during pandemic-induced lockdowns

Background Implementing a lockdown for disease mitigation is a balancing act: Nonpharmaceutical interventions can reduce disease transmission significantly, but interventions also have considerable societal costs. Therefore, decision-makers need near real-time information to calibrate the level of restrictions.Methods We fielded daily surveys in Denmark during the second wave of the COVID-19 pandemic to monitor public response to the announced lockdown. A key question asked respondents to state their number of close contacts within the past 24 hours. Here, we establish a link between survey data, mobility data, and hospitalizations via epidemic modelling of a short time-interval around Denmark’s December 2020 lockdown. Using Bayesian analysis, we then evaluate the usefulness of survey responses as a tool to monitor the effects of lockdown and then compare the predictive performance to that of mobility data.Results We find that, unlike mobility, self-reported contacts decreased significantly in all regions before the nation-wide implementation of non-pharmaceutical interventions and improved predicting future hospitalizations compared to mobility data. A detailed analysis of contact types indicates that contact with friends and strangers outperforms contact with colleagues and family members (outside the household) on the same prediction task.Conclusions Representative surveys thus qualify as a reliable, non-privacy invasive monitoring tool to track the implementation of non-pharmaceutical interventions and studypotential transmission paths

Contact-Based model for epidemic spreading on temporal networks

We present a contact-based model to study the spreading of epidemics by means of extending the dynamic message-passing approach to temporal networks. The shift in perspective from node- to edgecentric quantities enables accurate modeling of Markovian susceptible-infected-recovered outbreaks on time-varying trees, i.e., temporal networks with a loop-free underlying topology. On arbitrary graphs, the proposed contact-based model incorporates potential structural and temporal heterogeneities of the contact network and improves analytic estimations with respect to the individual-based (node-centric) approach at a low computational and conceptual cost. Within this new framework, we derive an analytical expression for the epidemic threshold on temporal networks and demonstrate the feasibility of this method on empirical data

Comparison between the temporal networks and the time aggregated networks.

<p>Comparison between the temporal networks and the time aggregated networks.</p

Transitivity is not assured in temporal networks.

<p>Here, links 1 → 2 and 2 → 3 exist, but the temporal order (1 → 2 at time <i>t</i> = 1 and 2 → 3 at time <i>t</i> = 0) prevents information to spread from node 1 to 3.</p