Epidemics on dynamic networks

Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model

We study the behavior of the eigenvectors associated with the smallest eigenvalues of the Laplacian matrix of temporal networks. We consider the multilayer representation of temporal networks, i.e., a set of networks linked through ordinal interconnected layers. We analyze the Laplacian matrix, known as supra-Laplacian, constructed through the supraadjacency matrix associated with the multilayer formulation of temporal networks, using a constant block Jacobi model which has closed-form solution. To do this, we assume that the interlayer weights are perturbations of the Kronecker sum of the separate adjacency matrices forming the temporal network. Thus we investigate the properties of the eigenvectors associated with the smallest eigenvalues (close to zero) of the supra-Laplacian matrix. Using arguments of perturbation theory, we show that these eigenvectors can be approximated by linear combinations of the zero eigenvectors of the individual time layers. This finding is crucial in reconsidering and generalizing the role of the Fielder vector in supra-Laplacian matrices.

Static graph approximations of dynamic contact networks for epidemic forecasting

Epidemic modeling is essential in understanding the spread of infectious diseases like COVID-19 and devising effective intervention strategies to control them. Recently, network-based disease models have integrated traditional compartment-based modeling with real-world contact graphs and shown promising results. However, in an ongoing epidemic, future contact network patterns are not observed yet. To address this, we use aggregated static networks to approximate future contacts for disease modeling. The standard method in the literature concatenates all edges from a dynamic graph into one collapsed graph, called the full static graph. However, the full static graph often leads to severe overestimation of key epidemic characteristics. Therefore, we propose two novel static network approximation methods, DegMST and EdgeMST, designed to preserve the sparsity of real world contact network while remaining connected. DegMST and EdgeMST use the frequency of temporal edges and the node degrees respectively to preserve sparsity. Our analysis show that our models more closely resemble the network characteristics of the dynamic graph compared to the full static ones. Moreover, our analysis on seven real-world contact networks suggests EdgeMST yield more accurate estimations of disease dynamics for epidemic forecasting when compared to the standard full static method.

Evaluating the dynamic interplay of social distancing policies regarding airborne pathogens through a temporal interaction-driven model that uses real-world and synthetic data

OBJECTIVE

The recent SARS-CoV-2 pandemic has exhibited diverse patterns of spread across countries and communities, emphasizing the need to consider the underlying population dynamics in modeling its progression and the importance of evaluating the effectiveness of non-pharmaceutical intervention strategies in combating viral transmission within human communities. Such an understanding requires accurate modeling of the interplay between the community dynamics and the disease propagation dynamics within the community.

METHODS

We build on an interaction-driven model of an airborne disease over contact networks that we have defined. Using the model, we evaluate the effectiveness of temporal, spatial, and spatiotemporal social distancing policies. Temporal social distancing involves a pure dilation of the timeline while preserving individual activity potential and thus prolonging the period of interaction; spatial distancing corresponds to social distancing pods; and spatiotemporal distancing pertains to the situation in which fixed subgroups of the overall group meet at alternate times. We evaluate these social distancing policies over real-world interactions' data and over history-preserving synthetic temporal random networks. Furthermore, we evaluate the policies for the disease's with different number of initial patients, corresponding to either the phase in the progression of the infection through a community or the number of patients infected together at the initial infection event. We expand our model to consider the exposure to viral load, which we correlate with the meetings' duration.

RESULTS

Our results demonstrate the superiority of decreasing social interactions (i.e., time dilation) within the community over partial isolation strategies, such as the spatial distancing pods and the spatiotemporal distancing strategy. In addition, we found that slow-spreading pathogens (i.e., pathogens that require a longer exposure to infect) spread roughly at the same rate as fast-spreading ones in highly active communities. This result is surprising since the pathogens may follow different paths. However, we demonstrate that the dilation of the timeline considerably slows the spread of the slower pathogens.

CONCLUSIONS

Our results demonstrate that the temporal dynamics of a community have a more significant effect on the spread of the disease than the characteristics of the spreading processes.

The aquaculture disease network model (AquaNet-Mod): A simulation model to evaluate disease spread and controls for the salmonid industry in England and Wales

Infectious disease causes significant mortality in wild and farmed systems, threatening biodiversity, conservation and animal welfare, as well as food security. To mitigate impacts and inform policy, tools such as mathematical models and computer simulations are valuable for predicting the potential spread and impact of disease. This paper describes the development of the Aquaculture Disease Network Model, AquaNet-Mod, and demonstrates its application to evaluating disease epidemics and the efficacy of control, using a Viral Haemorrhagic Septicaemia (VHS) case study. AquaNet-Mod is a data-driven, stochastic, state-transition model. Disease spread can occur via four different mechanisms, i) live fish movement, ii) river based, iii) short distance mechanical and iv) distance independent mechanical. Sites transit between three disease states: susceptible, clinically infected and subclinically infected. Disease spread can be interrupted by the application of disease mitigation measures and controls such as contact tracing, culling, fallowing and surveillance. Results from a VHS case study highlight the potential for VHS to spread to 96% of sites over a 10 year time horizon if no disease controls are applied. Epidemiological impact is significantly reduced when live fish movement restrictions are placed on the most connected sites and further still, when disease controls, representative of current disease control policy in England and Wales, are applied. The importance of specific disease control measures, particularly contact tracing and disease detection rate, are also highlighted. The merit of this model for evaluation of disease spread and the efficacy of controls, in the context of policy, along with potential for further application and development of the model, for example to include economic parameters, is discussed.

Assessing individual risk and the latent transmission of COVID-19 in a population with an interaction-driven temporal model

Interaction-driven modeling of diseases over real-world contact data has been shown to promote the understanding of the spread of diseases in communities. This temporal modeling follows the path-preserving order and timing of the contacts, which are essential for accurate modeling. Yet, other important aspects were overlooked. Various airborne pathogens differ in the duration of exposure needed for infection. Also, from the individual perspective, Covid-19 progression differs between individuals, and its severity is statistically correlated with age. Here, we enrich an interaction-driven model of Covid-19 and similar airborne viral diseases with (a) meetings duration and (b) personal disease progression. The enriched model enables predicting outcomes at both the population and the individual levels. It further allows predicting individual risk of engaging in social interactions as a function of the virus characteristics and its prevalence in the population. We further showed that the enigmatic nature of asymptomatic transmission stems from the latent effect of the network density on this transmission and that asymptomatic transmission has a substantial impact only in sparse communities.

Local and wide-scale livestock movement networks inform disease control strategies in East Africa

Livestock mobility exacerbates infectious disease risks across sub-Saharan Africa, but enables critical access to grazing and water resources, and trade. Identifying locations of high livestock traffic offers opportunities for targeted control. We focus on Tanzanian agropastoral and pastoral communities that account respectively for over 75% and 15% of livestock husbandry in eastern Africa. We construct networks of livestock connectivity based on participatory mapping data on herd movements reported by village livestock keepers as well as data from trading points to understand how seasonal availability of resources, land-use and trade influence the movements of livestock. In communities that practise agropastoralism, inter- and intra-village connectivity through communal livestock resources (e.g. pasture and water) was 1.9 times higher in the dry compared to the wet season suggesting greater livestock traffic and increased contact probability. In contrast, livestock from pastoral communities were 1.6 times more connected at communal locations during the wet season when they also tended to move farther (by 3 km compared to the dry season). Trade-linked movements were twice more likely from rural to urban locations. Urban locations were central to all networks, particularly those with potentially high onward movements, for example to abattoirs, livestock holding grounds, or other markets, including beyond national boundaries. We demonstrate how livestock movement information can be used to devise strategic interventions that target critical livestock aggregation points (i.e. locations of high centrality values) and times (i.e. prior to and after the wet season in pastoral and agropastoral areas, respectively). Such targeted interventions are a cost-effective approach to limit infection without restricting livestock mobility critical to sustainable livelihoods.

Dynamic Epidemiological Networks: A Data Representation Framework for Modeling and Tracking of SARS-CoV-2 Variants

The large-scale real-time sequencing of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) genomes has allowed for rapid identification of concerning variants through phylogenetic analysis. However, the nature of phylogenetic reconstruction is typically static, in that the relationships between taxonomic units, once defined, are not subject to alterations. Furthermore, most phylogenetic methods are intrinsically batch mode in nature, requiring the presence of the entire data set. Finally, the emphasis of phylogenetics is on relating taxonomical units. These characteristics complicate the application of classical phylogenetics methods to represent relationships in molecular data collected from rapidly evolving strains of an etiological agent, such as SARS-CoV-2, since the molecular landscape is updated continuously as samples are collected. In such settings, variant definitions are subject to epistemological constraints and may change as data accumulate. Furthermore, representing within-variant molecular relationships may be as important as representing between variant relationships. This article describes a novel data representation framework called dynamic epidemiological networks (DENs) along with algorithms that underpin its construction to address these issues. The proposed representation is applied to study the molecular development underlying the spread of the COVID-19 (coronavirus disease 2019) pandemic in two countries: Israel and Portugal spanning a 2-year period from February 2020 to April 2022. The results demonstrate how this framework could be used to provide a multiscale representation of the data by capturing molecular relationships between samples as well as those between variants, automatically identifying the emergence of high frequency variants (lineages), including variants of concern such as Alpha and Delta, and tracking their growth. Additionally, we show how analyzing the evolution of the DEN can help identify changes in the viral population that could not be readily inferred from phylogenetic analysis.

Temporal networks in biology and medicine: a survey on models, algorithms, and tools

The use of static graphs for modelling and analysis of biological and biomedical data plays a key role in biomedical research. However, many real-world scenarios present dynamic behaviours resulting in both node and edges modification as well as feature evolution. Consequently, ad-hoc models for capturing these evolutions along the time have been introduced, also referred to as dynamic, temporal, time-varying graphs. Here, we focus on temporal graphs, i.e., graphs whose evolution is represented by a sequence of time-ordered snapshots. Each snapshot represents a graph active in a particular timestamp. We survey temporal graph models and related algorithms, presenting fundamentals aspects and the recent advances. We formally define temporal graphs, focusing on the problem setting and we present their main applications in biology and medicine. We also present temporal graph embedding and the application to recent problems such as epidemic modelling. Finally, we further state some promising research directions in the area. Main results of this study include a systematic review of fundamental temporal network problems and their algorithmic solutions considered in the literature, in particular those having application in computational biology and medicine. We also include the main software developed in this context.

The Trade-Off between Airborne Pandemic Control and Energy Consumption Using Air Ventilation Solutions

Airborne diseases cause high mortality and adverse socioeconomic consequences. Due to urbanization, more people spend more time indoors. According to recent research, air ventilation reduces long-range airborne transmission in indoor settings. However, air ventilation solutions often incur significant energy costs and ecological footprints. The trade-offs between energy consumption and pandemic control indoors have not yet been thoroughly analyzed. In this work, we use advanced sensors to monitor the energy consumption and pandemic control capabilities of an air-conditioning system, a pedestal fan, and an open window in hospital rooms, classrooms, and conference rooms. A simulation of an indoor airborne pandemic spread of Coronavirus (COVID-19) is used to analyze the Pareto front. For the three examined room types, the Pareto front consists of all three air ventilation solutions, with some ventilation configurations demonstrating significant inefficiencies. Specifically, air-conditioning is found to be efficient only at a very high energy cost and fans seem to pose a reasonable alternative. To conclude, a more informed ventilation policy can bring about a more desirable compromise between energy consumption and pandemic spread control.

Modeling infectious disease dynamics: Integrating contact tracing-based stochastic compartment and spatio-temporal risk models

Major infectious diseases such as COVID-19 have a significant impact on population lives and put enormous pressure on healthcare systems globally. Strong interventions, such as lockdowns and social distancing measures, imposed to prevent these diseases from spreading, may also negatively impact society, leading to jobs losses, mental health problems, and increased inequalities, making crucial the prioritization of riskier areas when applying these protocols. The modeling of mobility data derived from contact-tracing data can be used to forecast infectious trajectories and help design strategies for prevention and control. In this work, we propose a new spatial-stochastic model that allows us to characterize the temporally varying spatial risk better than existing methods. We demonstrate the use of the proposed model by simulating an epidemic in the city of Valencia, Spain, and comparing it with a contact tracing-based stochastic compartment reference model. The results show that, by accounting for the spatial risk values in the model, the peak of infected individuals, as well as the overall number of infected cases, are reduced. Therefore, adding a spatial risk component into compartment models may give finer control over the epidemic dynamics, which might help the people in charge to make better decisions.

Analysis of the competition among viral strains using a temporal interaction-driven contagion model

The temporal dynamics of social interactions were shown to influence the spread of disease. Here, we model the conditions of progression and competition for several viral strains, exploring various levels of cross-immunity over temporal networks. We use our interaction-driven contagion model and characterize, using it, several viral variants. Our results, obtained on temporal random networks and on real-world interaction data, demonstrate that temporal dynamics are crucial to determining the competition results. We consider two and three competing pathogens and show the conditions under which a slower pathogen will remain active and create a second wave infecting most of the population. We then show that when the duration of the encounters is considered, the spreading dynamics change significantly. Our results indicate that when considering airborne diseases, it might be crucial to consider the duration of temporal meetings to model the spread of pathogens in a population.

How do mobility restrictions and social distancing during COVID-19 affect oil price?

This paper provides an analysis of the effect of the COVID-19 outbreak on the crude oil price. Using a newly developed air mobility index and Apple's driving trends index, we assess the effect of human mobility restrictions and social distancing during the COVID-19 pandemic on the crude oil price. We apply a quantile regression model, which evaluates different quantiles of the crude oil price. We also conduct an extreme value modeling, which examines the lower tail of the crude oil price distribution. We find that both the air mobility index and driving trends index significantly influence lower and upper quantiles of the WTI crude oil price. The extreme value models suggest that there is a potential risk of a negative crude oil price for a sudden extreme fall of air mobility.

A model for leveraging animal movement to understand spatio-temporal disease dynamics

The ongoing explosion of fine-resolution movement data in animal systems provides a unique opportunity to empirically quantify spatial, temporal and individual variation in transmission risk and improve our ability to forecast disease outbreaks. However, we lack a generalizable model that can leverage movement data to quantify transmission risk and how it affects pathogen invasion and persistence on heterogeneous landscapes. We developed a flexible model 'Movement-driven modelling of spatio-temporal infection risk' (MoveSTIR) that leverages diverse data on animal movement to derive metrics of direct and indirect contact by decomposing transmission into constituent processes of contact formation and duration and pathogen deposition and acquisition. We use MoveSTIR to demonstrate that ignoring fine-scale animal movements on actual landscapes can mis-characterize transmission risk and epidemiological dynamics. MoveSTIR unifies previous work on epidemiological contact networks and can address applied and theoretical questions at the nexus of movement and disease ecology.

Impacts of COVID-19 local spread and Google search trend on the US stock market

We develop a novel temporal complex network approach to quantify the US county level spread dynamics of COVID-19. We use both conventional econometric and Machine Learning (ML) models that incorporate the local spread dynamics, COVID-19 cases and death, and Google search activities to assess if incorporating information about local spreads improves the predictive accuracy of models for the US stock market. The results suggest that COVID-19 cases and deaths, its local spread, and Google searches have impacts on abnormal stock prices between January 2020 to May 2020. Furthermore, incorporating information about local spread significantly improves the performance of forecasting models of the abnormal stock prices at longer forecasting horizons.

Evaluating strategies for spatial allocation of vaccines based on risk and centrality

When vaccinating a large population in response to an invading pathogen, it is often necessary to prioritize some individuals to be vaccinated first. One way to do this is to choose individuals to vaccinate based on their location. Methods for this prioritization include strategies that target those regions most at risk of importing the pathogen, and strategies that target regions with high centrality on the travel network. We use a simple infectious disease epidemic model to compare a risk-targeting strategy to two different centrality-targeting strategies based on betweenness centrality and random walk percolation centrality, respectively. We find that the relative effectiveness of these strategies in reducing the total number of infections varies with the basic reproduction number of the pathogen, travel rates, structure of the travel network and vaccine availability. We conclude that when a pathogen has high spreading capacity, or when vaccine availability is limited, centrality-targeting strategies should be considered as an alternative to the more commonly used risk-targeting strategies.

Preventive effect of on-farm biosecurity practices against highly pathogenic avian influenza (HPAI) H5N6 infection on commercial layer farms in the Republic of Korea during the 2016-17 epidemic: A case-control study

Highly pathogenic avian influenza virus (HPAIv) H5N6 has destructive consequences on the global poultry production system. Recently, a growing number of layer farms have been heavily damaged from the HPAIv epidemic due to the increased virulence of the virus and the intensification of the production system. Therefore, stakeholders should implement effective preventive practices at the farm level that are aligned with contingency measures at the national level to minimize poultry losses. However, numerous biosecurity protocols for layer farm workers to follow have been developed, impeding efficient prevention and control. Furthermore, the effectiveness of biosecurity practices varies with the geographical condition and inter-farm contact structures. Hence, the objective of our study was to examine the preventive effect of five biosecurity actions commonly practiced at layer farms in the Republic of Korea against HPAIv H5N6: (i) fence installation around a farm, ii) rodent control inside a farm; iii) disinfection booth for visitors for disinfection protocols, iv) an anterior room in the sheds before entering the bird area and v) boots changes when moving between sheds in the same farm. We conducted a case-control study on 114 layer case farms and 129 layer control farms during the 2016-17 HPAI epidemic. The odds ratios for five on-farm biosecurity practices implemented in those study groups were estimated as a preventive effect on the HPAI infection with covariates, including seven geographical conditions and three network metrics using Bayesian hierarchical logistic regression and geographical location weighted logistic regression. The results showed that the use of a disinfection booth for personnel reduced the odds of HPAIv H5N6 infection (adjusted odds ratio [AOR] = 0.002, 95 % credible interval [CrI] = 0.00007 - 0.025) with relatively small spatial variation (minimum AOR - maximum AOR: 0.084-0.263). Changing boots between sheds on the same farm reduced the odds of HPAIv H5N6 infection (AOR = 0.160, 95 % CrI = 0.024-0.852) with relatively wide spatial variation (minimum AOR - maximum AOR = 0.270-0.688). Therefore, enhanced personnel biosecurity protocols at the farm of entry for layer farms is recommended to effectively prevent and respond to HPAIv H5N6 infection under different local condition. Our study provides an important message for layer farmers to effectively implement on-farm biosecurity actions against HPAIv H5N6 infection at their farms by setting priorities based on their spatial condition and network position.

Multihazards Scenario Generator: A Network-Based Simulation of Natural Disasters

The impact of natural disasters has been increasing in recent years. Despite the developing international interest in multihazard events, few studies quantify the dynamic interactions that characterize these phenomena. It is argued that without considering the dynamic complexity of natural catastrophes, impact assessments will underestimate risk and misinform emergency management priorities. The ability to generate multihazard scenarios with impacts at a desired level is important for emergency planning and resilience assessment. This article demonstrates a framework for using graph theory and networks to generate and model the complex impacts of multihazard scenarios. First, the combination of maximal hazard footprints and exposed nodes (e.g., infrastructure) is used to create the hazard network. Iterative simulation of the network, defined by actual hazard magnitudes, is then used to provide the overall compounded impact from a sequence of hazards. Outputs of the method are used to study distributional ranges of multihazards impact. The 2016 Kaikōura earthquake is used as a calibrating event to demonstrate that the method can reproduce the same scale of impacts as a real event. The cascading hazards included numerous landslides, allowing us to show that the scenario set generated includes the actual impacts that occurred during the 2016 events.

Contextual contact tracing based on stochastic compartment modeling and spatial risk assessment

The current situation of COVID-19 highlights the paramount importance of infectious disease surveillance, which necessitates early monitoring for effective response. Policymakers are interested in data insights identifying high-risk areas as well as individuals to be quarantined, especially as the public gets back to their normal routine. We investigate both requirements by the implementation of disease outbreak modeling and exploring its induced dynamic spatial risk in form of risk assessment, along with its real-time integration back into the disease model. This paper implements a contact tracing-based stochastic compartment model as a baseline, to further modify the existing setup to include the spatial risk. This modification of each individual-level contact's intensity to be dependent on its spatial location has been termed as Contextual Contact Tracing. The results highlight that the inclusion of spatial context tends to send more individuals into quarantine which reduces the overall spread of infection. With a simulated example of an induced spatial high-risk, it is highlighted that the new spatio-SIR model can act as a tool to empower the analyst with a capability to explore disease dynamics from a spatial perspective. We conclude that the proposed spatio-SIR tool can be of great help for policymakers to know the consequences of their decision prior to their implementation.

Impact of temporal correlations on high risk outbreaks of independent and cooperative SIR dynamics

We first propose a quantitative approach to detect high risk outbreaks of independent and coinfective SIR dynamics on three empirical networks: a school, a conference and a hospital contact network. This measurement is based on the k-means clustering method and identifies proper samples for calculating the mean outbreak size and the outbreak probability. Then we systematically study the impact of different temporal correlations on high risk outbreaks over the original and differently shuffled counterparts of each network. We observe that, on the one hand, in the coinfection process, randomization of the sequence of the events increases the mean outbreak size of high-risk cases. On the other hand, these correlations do not have a consistent effect on the independent infection dynamics, and can either decrease or increase this mean. Randomization of the daily pattern correlations has no strong impact on the size of the outbreak in either the coinfection or the independent spreading cases. We also observe that an increase in the mean outbreak size does not always coincide with an increase in the outbreak probability; therefore, we argue that merely considering the mean outbreak size of all realizations may lead us into falsely estimating the outbreak risks. Our results suggest that some sort of contact randomization in the organizational level in schools, events or hospitals might help to suppress the spreading dynamics while the risk of an outbreak is high.

Concurrency measures in the era of temporal network epidemiology: a review

Diseases spread over temporal networks of interaction events between individuals. Structures of these temporal networks hold the keys to understanding epidemic propagation. One early concept of the literature to aid in discussing these structures is concurrency-quantifying individuals' tendency to form time-overlapping 'partnerships'. Although conflicting evaluations and an overabundance of operational definitions have marred the history of concurrency, it remains important, especially in the area of sexually transmitted infections. Today, much of theoretical epidemiology uses more direct models of contact patterns, and there is an emerging body of literature trying to connect methods to the concurrency literature. In this review, we will cover the development of the concept of concurrency and these new approaches.

Temporal stability of swine movement networks in the U.S

As a consequence of multi-site pig production practiced in North America, frequent and widespread animal movements create extensive networks of interaction between farms. Social network analysis (SNA) has been used to understand disease transmission risks within these complex and dynamic production ecosystems and is particularly relevant for designing risk-based surveillance and control strategies targeting highly connected farms. However, inferences from SNA and the effectiveness of targeted strategies may be influenced by temporal changes in network structure. Since farm movements represent a temporally dynamic network, it is also unclear how many months of data are required to gain an accurate picture of an individual farm's connectivity pattern and the overall network structure. The extent to which shipments between two specific farms are repeated (i.e., "loyalty" of farm contacts) can influence the rate at which the structure of a network changes over time, which may influence disease dynamics. In this study, we aimed to describe temporal stability and loyalty patterns of pig movement networks in the U.S. swine industry. We analyzed a total of 282,807 animal movements among 2724 farms belonging to two production systems between 2014 and 2017. Loyalty trends were largely driven by contacts between sow farms and nurseries and between nurseries and finisher farms; mean loyalty (percent of contacts that were repeated at least once within a 52-week interval) of farm contacts was 51-60 % for farm contacts involving weaned pigs, and 12-22% for contacts involving feeder pigs. A cyclic pattern was observed for both weaned and feeder pig movements, with episodes of increased loyalty observed at intervals of 8 and 17-20 weeks, respectively. Network stability was achieved when six months of data were aggregated, and only small shifts in node-level and global network metrics were observed when adding more data. This stability is relevant for designing targeted surveillance programs for disease management, given that movements summarized over too short a period may lead to stochastic swings in network metrics. A temporal resolution of six months would be reliable for the identification of potential super-spreaders in a network for targeted intervention and disease control. The temporal stability observed in these networks suggests that identifying highly connected farms in retrospective network data (up to 24 months) is reliable for future planning, albeit with reduced effectiveness.

Simulation-based evaluation of school reopening strategies during COVID-19: A case study of São Paulo, Brazil

During the coronavirus disease 2019 (COVID-19) pandemic, many countries opted for strict public health measures, including closing schools. After some time, they have started relaxing some of those restrictions. To avoid overwhelming health systems, predictions for the number of new COVID-19 cases need to be considered when choosing a school reopening strategy. Using a computer simulation based on a stochastic compartmental model that includes a heterogeneous and dynamic network, we analyse different strategies to reopen schools in the São Paulo Metropolitan Area, including one similar to the official reopening plan. Our model allows us to describe different types of relations between people, each type with a different infectiousness. Based on our simulations and model assumptions, our results indicate that reopening schools with all students at once has a big impact on the number of new COVID-19 cases, which could cause a collapse of the health system. On the other hand, our results also show that a controlled school reopening could possibly avoid the collapse of the health system, depending on how people follow sanitary measures. We estimate that postponing the schools' return date for after a vaccine becomes available may save tens of thousands of lives just in the São Paulo Metropolitan Area compared to a controlled reopening considering a worst-case scenario. We also discuss our model constraints and the uncertainty of its parameters.

High infectiousness immediately before COVID-19 symptom onset highlights the importance of continued contact tracing

Background

Understanding changes in infectiousness during SARS-COV-2 infections is critical to assess the effectiveness of public health measures such as contact tracing.

Methods

Here, we develop a novel mechanistic approach to infer the infectiousness profile of SARS-COV-2-infected individuals using data from known infector-infectee pairs. We compare estimates of key epidemiological quantities generated using our mechanistic method with analogous estimates generated using previous approaches.

Results

The mechanistic method provides an improved fit to data from SARS-CoV-2 infector-infectee pairs compared to commonly used approaches. Our best-fitting model indicates a high proportion of presymptomatic transmissions, with many transmissions occurring shortly before the infector develops symptoms.

Conclusions

High infectiousness immediately prior to symptom onset highlights the importance of continued contact tracing until effective vaccines have been distributed widely, even if contacts from a short time window before symptom onset alone are traced.

Funding

Engineering and Physical Sciences Research Council (EPSRC).

Spread of Epidemic Disease on Edge-Weighted Graphs from a Database: A Case Study of COVID-19

The understanding of infectious diseases is a priority in the field of public health. This has generated the inclusion of several disciplines and tools that allow for analyzing the dissemination of infectious diseases. The aim of this manuscript is to model the spreading of a disease in a population that is registered in a database. From this database, we obtain an edge-weighted graph. The spreading was modeled with the classic SIR model. The model proposed with edge-weighted graph allows for identifying the most important variables in the dissemination of epidemics. Moreover, a deterministic approximation is provided. With database COVID-19 from a city in Chile, we analyzed our model with relationship variables between people. We obtained a graph with 3866 vertices and 6,841,470 edges. We fitted the curve of the real data and we have done some simulations on the obtained graph. Our model is adjusted to the spread of the disease. The model proposed with edge-weighted graph allows for identifying the most important variables in the dissemination of epidemics, in this case with real data of COVID-19. This valuable information allows us to also include/understand the networks of dissemination of epidemics diseases as well as the implementation of preventive measures of public health. These findings are important in COVID-19's pandemic context.

Lessons from movement ecology for the return to work: Modeling contacts and the spread of COVID-19

Human behavior (movement, social contacts) plays a central role in the spread of pathogens like SARS-CoV-2. The rapid spread of SARS-CoV-2 was driven by global human movement, and initial lockdown measures aimed to localize movement and contact in order to slow spread. Thus, movement and contact patterns need to be explicitly considered when making reopening decisions, especially regarding return to work. Here, as a case study, we consider the initial stages of resuming research at a large research university, using approaches from movement ecology and contact network epidemiology. First, we develop a dynamical pathogen model describing movement between home and work; we show that limiting social contact, via reduced people or reduced time in the workplace are fairly equivalent strategies to slow pathogen spread. Second, we develop a model based on spatial contact patterns within a specific office and lab building on campus; we show that restricting on-campus activities to labs (rather than labs and offices) could dramatically alter (modularize) contact network structure and thus, potentially reduce pathogen spread by providing a workplace mechanism to reduce contact. Here we argue that explicitly accounting for human movement and contact behavior in the workplace can provide additional strategies to slow pathogen spread that can be used in conjunction with ongoing public health efforts.

GoCoronaGo: Privacy Respecting Contact Tracing for COVID-19 Management

The COVID-19 pandemic is imposing enormous global challenges in managing the spread of the virus. A key pillar to mitigation is contact tracing, which complements testing and isolation. Digital apps for contact tracing using Bluetooth technology available in smartphones have gained prevalence globally. In this article, we discuss various capabilities of such digital contact tracing, and its implication on community safety and individual privacy, among others. We further describe the GoCoronaGo institutional contact tracing app that we have developed, and the conscious and sometimes contrarian design choices we have made. We offer a detailed overview of the app, backend platform and analytics, and our early experiences with deploying the app to over 1000 users within the Indian Institute of Science campus in Bangalore. We also highlight research opportunities and open challenges for digital contact tracing and analytics over temporal networks constructed from them.

The Epidemiological Framework for Biological Invasions (EFBI): an interdisciplinary foundation for the assessment of biosecurity threats

Emerging microparasite (e.g. viruses, bacteria, protozoa and fungi) epidemics and the introduction of non-native pests and weeds are major biosecurity threats worldwide. The likelihood of these threats is often estimated from probabilities of their entry, establishment, spread and ease of prevention. If ecosystems are considered equivalent to hosts, then compartment disease models should provide a useful framework for understanding the processes that underpin non-native species invasions. To enable greater cross-fertilisation between these two disciplines, the Epidemiological Framework for Biological Invasions (EFBI) is developed that classifies ecosystems in relation to their invasion status: Susceptible, Exposed, Infectious and Resistant. These states are linked by transitions relating to transmission, latency and recovery. This viewpoint differs markedly from the species-centric approaches often applied to non-native species. It allows generalisations from epidemiology, such as the force of infection, the basic reproductive ratio R0, super-spreaders, herd immunity, cordon sanitaire and ring vaccination, to be discussed in the novel context of non-native species and helps identify important gaps in the study of biological invasions. The EFBI approach highlights several limitations inherent in current approaches to the study of biological invasions including: (i) the variance in non-native abundance across ecosystems is rarely reported; (ii) field data rarely (if ever) distinguish source from sink ecosystems; (iii) estimates of the susceptibility of ecosystems to invasion seldom account for differences in exposure to non-native species; and (iv) assessments of ecosystem susceptibility often confuse the processes that underpin patterns of spread within -and between- ecosystems. Using the invasion of lakes as a model, the EFBI approach is shown to present a new biosecurity perspective that takes account of ecosystem status and complements demographic models to deliver clearer insights into the dynamics of biological invasions at the landscape scale. It will help to identify whether management of the susceptibility of ecosystems, of the number of vectors, or of the diversity of pathways (for movement between ecosystems) is the best way of limiting or reversing the population growth of a non-native species. The framework can be adapted to incorporate increasing levels of complexity and realism and to provide insights into how to monitor, map and manage biological invasions more effectively.

Characterization of potential superspreader farms for bovine tuberculosis: A review

Background

Variation in host attributes that influence their contact rates and infectiousness can lead some individuals to make disproportionate contributions to the spread of infections. Understanding the roles of such ‘superspreaders’ can be crucial in deciding where to direct disease surveillance and controls to greatest effect. In the epidemiology of bovine tuberculosis (bTB) in Great Britain, it has been suggested that a minority of cattle farms or herds might make disproportionate contributions to the spread of Mycobacterium bovis, and hence might be considered ‘superspreader farms’.

Objectives and Methods

We review the literature to identify the characteristics of farms that have the potential to contribute to exceptional values in the three main components of the farm reproductive number ‐ R_f: contact rate, infectiousness and duration of infectiousness, and therefore might characterize potential superspreader farms for bovine tuberculosis in Great Britain.

Results

Farms exhibit marked heterogeneity in contact rates arising from between‐farm trading of cattle. A minority of farms act as trading hubs that greatly augment connections within cattle trading networks. Herd infectiousness might be increased by high within‐herd transmission or the presence of supershedding individuals, or infectiousness might be prolonged due to undetected infections or by repeated local transmission, via wildlife or fomites.

Conclusions

Targeting control methods on putative superspreader farms might yield disproportionate benefits in controlling endemic bovine tuberculosis in Great Britain. However, real‐time identification of any such farms, and integration of controls with industry practices, present analytical, operational and policy challenges.

Implications of farmed-cervid movements on the transmission of chronic wasting disease

Chronic wasting disease is a transmissible spongiform encephalopathy that affects cervids with a clinical picture of muscle wasting in infected animals. The objective of this study was to quantify movement patterns of farmed cervids in the state of Minnesota as a model for identifying potential disease mitigation points. Time aggregated network analysis was performed on data consisting of 1221 intra-state cervid movements from farms located within Minnesota (n = 432 farms). Intra-state movements accounted for 48.2 % of all documented movements (2578) in Minnesota from 2013 to 2018; the remaining movements were inter-state. Annual networks were sparse in nature with low graph densities (6.9 × 10^-4 - 1.4 × 10^-3) and transitivity (0.06-0.12). Frequency of movements increased significantly (p < 0.05) in the months of September and October before decreasing in November, which coincided with the breeding and hunting seasons. Some of these contacts were as far as 500 km apart. The median length of infection chains for CWD positive farms was estimated to be 5.0 and 6.0 farms in-and out-going infection chains, respectively. A k-test analysis demonstrated that the observed median number of infected farms directly connected to other infected farms was 2.0, which was significantly higher than a fortuitous event (p = 0.002). Movements of cervids between farms were largely unpredictable with very low edge overlap (mean 0.02 %) from year to year, suggesting that persistent commercial relationships among farms were rare. In conclusion, long distance trade movements present a risk for spread of chronic wasting disease in Minnesota. The sparse networks and unpredictable farm contacts could be because cervid production is not as vertically integrated as other species-differentiated and established industries, such as swine or poultry. Our analytical approach can be used to understand chronic wasting disease in other states in the U.S. and North America in general.

Key Challenges in Modelling an Epidemic - What have we Learned from the COVID-19 Epidemic so Far

Mathematical modelling can be useful for predicting how infectious diseases progress, enabling us to show the likely outcome of an epidemic and help inform public health interventions. Different modelling techniques have been used to predict and simulate the spread of COVID-19, but they have not always been useful for epidemiologists and decision-makers. To improve the reliability of the modelling results, it is very important to critically evaluate the data used and to check whether or not due regard has been paid to the different ways in which the disease spreads through the population. As building an epidemiological model that is reliable enough and suits the current epidemiological situation within a country or region, certain criteria must be met in the modelling process. It might be necessary to use a combination of two or more different types of models in order to cover all aspects of epidemic modelling. If we want epidemiological models to be a useful tool in combating the epidemic, we need to engage experts from epidemiology, data science and statistics.

Identification of critical airports for controlling global infectious disease outbreaks: Stress-tests focusing in Europe

As the global population increases and transportation connectivity improves in quality and prices, the demand for mobility increases, especially in long-haul services. According to the 2017 report of the European Commission in Mobility and Transport, the performance of all modes for passenger transport (roadways and airways) are reaching record highs. Although the benefits of the increased demand for mobility are substantial and welcome, an effort should be paid such as to ameliorate possible threatening side-effects that may also arise. As World Health Organization (WHO) denotes and as has been evident from the global COVID-19 epidemic outbreak, infectious diseases can be spread directly or indirectly from one person to another under common exposure circumstances such as air transportation (especially long-haul airline connections) that may act as the medium for transmitting and spreading infectious diseases. In this paper, analytical and realistic models have been integrated, for providing evidence on the spread dynamics of infectious diseases that may face Europe through the airlines system. In particular, a detailed epidemiological model has been integrated with the airlines' and land transport network, able to simulate the epidemic spread of infectious diseases originated from distant locations. Additionally, a wide set of experiments and simulations have been conducted, providing results from detailed stress-tests covering both mild as well as aggressive cases of epidemic spreading scenarios. The results provide convincing evidence on the effectiveness that the European airports' system offer in controlling the emergence of epidemics, but also on the time and extent that controlling measures should be taken in order to break the chain of infections in realistic cases.

A framework for second-order eigenvector centralities and clustering coefficients

We propose and analyse a general tensor-based framework for incorporating second-order features into network measures. This approach allows us to combine traditional pairwise links with information that records whether triples of nodes are involved in wedges or triangles. Our treatment covers classical spectral methods and recently proposed cases from the literature, but we also identify many interesting extensions. In particular, we define a mutually reinforcing (spectral) version of the classical clustering coefficient. The underlying object of study is a constrained nonlinear eigenvalue problem associated with a cubic tensor. Using recent results from nonlinear Perron-Frobenius theory, we establish existence and uniqueness under appropriate conditions, and show that the new spectral measures can be computed efficiently with a nonlinear power method. To illustrate the added value of the new formulation, we analyse the measures on a class of synthetic networks. We also give computational results on centrality and link prediction for real-world networks.

Multilayer network analysis unravels haulage vehicles as a hidden threat to the British swine industry

When assessing the role of live animal trade networks in the spread of infectious diseases in livestock, attention has focused mainly on direct movements of animals between premises, whereas the role of haulage vehicles used during transport, an indirect route for disease transmission, has largely been ignored. Here, we have assessed the impact of sharing haulage vehicles from livestock transport service providers on the connectivity between farms as well as on the spread of swine infectious diseases in Great Britain (GB). Using all pig movement records between April 2012 and March 2014 in GB, we built a series of directed and weighted static multiplex networks consisting of two layers of identical nodes, where nodes (farms) are linked either by (a) the direct movement of pigs and (b) the shared use of haulage vehicles. The haulage contact definition integrates the date of the move and the duration Δ s that lorries are left contaminated by pathogens, hence accounting for the temporal aspect of contact events. For increasing Δ s , descriptive network analyses were performed to assess the role of haulage on network connectivity. We then explored how viruses may spread throughout the GB pig sector by computing the reproduction number R . Our results showed that sharing haulage vehicles increases the number of contacts between farms by >50% and represents an important driver of disease transmission. In particular, sharing haulage vehicles, even if Δ s  < 1 day, will limit the benefit of the standstill regulation, increase the number of premises that could be infected in an outbreak, and more easily raise R above 1. This work confirms that sharing haulage vehicles has significant potential for spreading infectious diseases within the pig sector. The cleansing and disinfection process of haulage vehicles is therefore a critical control point for disease transmission risk mitigation.

Analysing livestock network data for infectious disease control: an argument for routine data collection in emerging economies

Livestock movements are an important mechanism of infectious disease transmission. Where these are well recorded, network analysis tools have been used to successfully identify system properties, highlight vulnerabilities to transmission, and inform targeted surveillance and control. Here we highlight the main uses of network properties in understanding livestock disease epidemiology and discuss statistical approaches to infer network characteristics from biased or fragmented datasets. We use a 'hurdle model' approach that predicts (i) the probability of movement and (ii) the number of livestock moved to generate synthetic 'complete' networks of movements between administrative wards, exploiting routinely collected government movement permit data from northern Tanzania. We demonstrate that this model captures a significant amount of the observed variation. Combining the cattle movement network with a spatial between-ward contact layer, we create a multiplex, over which we simulated the spread of 'fast' ( R0 = 3) and 'slow' ( R0 = 1.5) pathogens, and assess the effects of random versus targeted disease control interventions (vaccination and movement ban). The targeted interventions substantially outperform those randomly implemented for both fast and slow pathogens. Our findings provide motivation to encourage routine collection and centralization of movement data to construct representative networks. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'. This theme issue is linked with the earlier issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'.

The contact structure of Great Britain's salmon and trout aquaculture industry

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87% of English and Welsh nodes are reachable from Scotland via the live fish movement network.

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72% of Scottish nodes are reachable from England or Wales via the live fish movement network.

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7.2% of all live fish movements cross the England-Scotland border.

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Targeted surveillance on a handful of sites is effective in identifying and controlling outbreaks.

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The combination of different mechanisms of transmission increases the chance of large epidemics.

We analyse the network structure of the British salmonid aquaculture industry from the perspective of infectious disease control. We combine for the first time live fish transport (or movement) data covering England and Wales with data covering Scotland and include network layers representing potential transmission by rivers, sea water and local transmission via human or animal vectors in the immediate vicinity of each farm or fishery site. We find that 7.2% of all live fish transports cross the England-Scotland border and network analysis shows that 87% of English and Welsh nodes and 72% of Scottish nodes are reachable from cross-border connections via live fish transports alone. Consequently, from a disease-control perspective, the contact structures of England and Wales and of Scotland should not be considered in isolation. We also show that large epidemics require the live fish movement network and so control strategies targeting movements can be very effective. While there is relatively low risk of widespread epidemics on the live fish transport network alone, the potential risk is substantially amplified by the combined interaction of multiple network layers.